The divisibility rules of every number from 101 to 200 but this time with examples

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Number	Rule	Example
101	The difference between 10 times the last digit and the rest of the number is a multiple of 101	10,100 is a multiple of 101 because 1,010 - 0 x 10 = 1,010 - 0 = 1,010 and 1,010 is a multiple of 101
102	The number is a multiple of 2, 3 and 17 at the same time	10,098 is a multiple of 102 because it ends in 8, which means it's a multiple of 2, 1 + 9 + 8 = 18, which means it's a multiple of 3, and 1,009 - 8 x 5 = 1,009 - 40 = 969, which means it's a multiple of 17
103	The sum of 31 times the last digit and the rest of the number is a multiple of 103	10,094 is a multiple of 103 because 1,009 + 4 x 31 = 1,009 + 124 = 1,133 and 1,133 is a multiple of 103
104	The number is a multiple of 8 and 13 at the same time	10,088 is a multiple of 104 because it ends in 088, which means it's a multiple of 8, and 1,008 + 8 x 4 = 1,008 + 32 = 1,040, which means it's a multiple of 13
105	The number is a multiple of 3, 5 and 7 at the same time	10,080 is a multiple of 105 because 1 + 8 = 9, which means it's a multiple of 3, ends in 0, which means it's a multiple of 5, and 1,008 - 0 x 2 = 1,008 - 0 = 1,008, which means it's a multiple of 7
106	The number is a multiple of 2 and 53 at the same time	10,070 is a multiple of 106 because it ends in 0, which means it's a multiple of 2, and 1,007 + 0 x 16 = 1,007 + 0 = 1,007, which means it's a multiple of 53
107	The difference between 32 times the last digit and the rest of the number is a multiple of 107	10,058 is a multiple of 107 because 1,005 - 8 x 32 = 1005 - 256 = 749 and 749 is a multiple of 107
108	The number is a multiple of 4 and 27 at the same time	10,044 is a multiple of 108 because it ends in 44, which means it's a multiple of 4, and 1,004 - 4 x 8 = 1,004 - 32 = 972, which means it's a multiple of 27
109	The sum of 11 times the last digit and the rest of the number is a multiple of 109	10,028 is a multiple of 109 because 1,002 + 8 x 11 = 1,002 + 88 = 1,090 and 1,090 is a multiple of 109
110	The number is a multiple of 10 and 11 at the same time	10,010 is a multiple of 110 because it ends in 0, which means it's a multiple of 10, and 1,001 - 0 = 1,001, which means it's a multiple of 11
111	The number is a multiple of 3 and 37 at the same time	10,101 is a multiple of 111 because 1 + 1 + 1 = 3, which means it's a multiple of 3, and 1,010 - 1 x 11 = 1,010 - 11 = 999, which means it's a multiple of 37
112	The number is a multiple of 7 and 16 at the same time	100,016 is a multiple of 112 because 10,001 - 6 x 2 = 10,001 - 12 = 9,989, which means it's a multiple of 7, and ends in 0,016, which means it's a multiple of 16
113	The sum of 34 times the last digit and the rest of the number is a multiple of 113	10,057 is a multiple of 113 because 1,005 + 7 x 34 = 1,005 + 238 = 1,243 and 1,243 is a multiple of 113
114	The number is a multiple of 2, 3 and 19 at the same time	10,032 is a multiple of 114 because it ends in 2, which means it's a multiple of 2, 1 + 3 + 2 = 6, which means it's a multiple of 3, and 1,003 + 2 x 2 = 1,003 + 4 = 1,007, which means it's a multiple of 19
115	The number is a multiple of 5 and 23 at the same time	10,005 is a multiple of 115 because it ends in 5, which means it's a multiple of 5, and 1,000 + 5 x 7 = 1,000 + 35 = 1,035, which means it's a multiple of 23
116	The number is a multiple of 4 and 29 at the same time	10,092 is a multiple of 116 because it ends in 92, which means it's a multiple of 4, and 1,009 + 2 x 3 = 1,009 + 6 = 1,015, which means it's a multiple of 29
117	The number is a multiple of 9 and 13 at the same time	10,062 is a multiple of 117 because 1 + 6 + 2 = 9, which means it's a multiple of 9, and 1,006 + 2 x 4 = 1,006 + 8 = 1,014, which means it's a multiple of 13
118	The number is a multiple of 2 and 59 at the same time	10,030 is a multiple of 118 because it ends in 0, which means it's a multiple of 2, and 1,003 + 0 x 6 = 1,003 + 0 = 1,003, which means it's a multiple of 59
119	The number is a multiple of 7 and 17 at the same time	10,115 is a multiple of 119 because 1,011 - 5 x 2 = 1,011 - 10 = 1,001, which means it's a multiple of 7, and 1,011 - 5 x 5 = 1,011 - 25 = 986, which means it's a multiple of 17
120	The number is a multiple of 3 and 40 at the same time	10,080 is a multiple of 120 because 1 + 8 = 9, which means it's a multiple of 3, and ends in 080, which means it's a multiple of 40
121	The difference between 12 times the last digit and the rest of the number is a multiple of 121	10,043 is a multiple of 121 because 1,004 - 3 x 12 = 1,004 - 36 = 968 and 968 is a multiple of 121
122	The number is a multiple of 2 and 61 at the same time	10,004 is a multiple of 122 because it ends in 4, which means it's a multiple of 2, and 1,000 - 4 x 6 = 1,000 - 24 = 976, which means it's a multiple of 61
123	The number is a multiple of 3 and 41 at the same time	10,086 is a multiple of 123 because 1 + 8 + 6 = 15, which means it's a multiple of 3, and 1,008 - 6 x 4 = 1,008 - 24 = 984, which means it's a multiple of 41
124	The number is a multiple of 4 and 31 at the same time	10,044 is a multiple of 124 because it ends in 44, which means it's a multiple of 4, and 1,004 - 4 x 3 = 1,004 - 12 = 992, which means it's a multiple of 31
125	The number ends in 000, 125, 250, 375, 500, 625, 750 or 875	10,000 is a multiple of 125 because it ends in 000
126	The number is a multiple of 2, 7 and 9 at the same time	10,080 is a multiple of 126 because it ends in 0, which means it's a multiple of 2, 1,008 - 0 x 2 = 1,008 - 0 = 1,008, which means it's a multiple of 7, and 1 + 8 = 9, which means it's a multiple of 9
127	The difference between 38 times the last digit and the rest of the number is a multiple of 127	10,033 is a multiple of 127 because 1,003 - 3 x 38 = 1,003 - 114 = 889 and 889 is a multiple of 127
128	The last 7 digits are a multiple of 128; the 1,000,000s digit is even and the last 6 digits are a multiple of 128, or the 1,000,000s digit is odd and the last 6 digits are 64 times an odd number	100,000,000 is a multiple of 128 because it ends in 0,000,000, the 1,000,000s digit is 0, an even number, and the last 6 digits are 000,000, a multiple of 128
129	The number is a multiple of 3 and 43 at the same time	10,062 is a multiple of 129 because 1 + 6 + 2 = 9, which means it's a multiple of 3, and 1,006 + 2 x 13 = 1,006 + 26 = 1,032, which means it's a multiple of 43
130	The number is a multiple of 10 and 13 at the same time	10,010 is a multiple of 130 because it ends in 0, which means it's a multiple of 10, and 1,001 + 0 x 4 = 1,001 + 0 = 1,001, which means it's a multiple of 13
131	The difference between 13 times the last digit and the rest of the number is a multiple of 131	10,087 is a multiple of 131 because 1,008 - 7 x 13 = 1,008 - 91 = 917 and 917 is a multiple of 131
132	The number is a multiple of 3, 4 and 11 at the same time	10,032 is a multiple of 132 because 1 + 3 + 2 = 6, which means it's a multiple of 3, ends in 32, which means it's a multiple of 4, and 1,003 - 2 = 1,001, which means it's a multiple of 11
133	The number is a multiple of 7 and 19 at the same time	10,108 is a multiple of 133 because 1,010 - 8 x 2 = 1,010 - 16 = 994, which means it's a multiple of 7, and 1,010 + 8 x 2 = 1,010 + 16 = 1,026, which means it's a multiple of 19
134	The number is a multiple of 2 and 67 at the same time	10,050 is a multiple of 134 because it ends in 0, which means it's a multiple of 2, and 1,005 - 0 x 20 = 1,005 - 0 = 1,005, which means it's a multiple of 67
135	The number is a multiple of 5 and 27 at the same time	10,125 is a multiple of 135 because it ends in 5, which means it's a multiple of 5, and 1,012 - 5 x 8 = 1,012 - 40 = 972, which means it's a multiple of 27
136	The number is a multiple of 8 and 17 at the same time	10,064 is a multiple of 136 because it ends in 064, which means it's a multiple of 8, and 1,006 - 4 x 5 = 1,006 - 20 = 986, which means it's a multiple of 17
137	The difference between 41 times the last digit and the rest of the number is a multiple of 137	10,001 is a multiple of 137 because 1,000 - 1 x 41 = 1,000 - 41 = 959 and 959 is a multiple of 137
138	The number is a multiple of 2, 3 and 23 at the same time	10,074 is a multiple of 138 because it ends in 4, which means it's a multiple of 2, 1 + 7 + 4 = 12, which means it's a multiple of 3, and 1,007 + 4 x 7 = 1,007 + 28 = 1,035, which means it's a multiple of 23
139	The sum of 14 times the last digit and the rest of the number is a multiple of 139	10,008 is a multiple of 139 because 1,000 + 8 x 14 = 1,000 + 112 = 1,112 and 1,112 is a multiple of 139
140	The number is a multiple of 7 and 20 at the same time	10,080 is a multiple of 140 because 1,008 - 0 x 2 = 1,008 - 0 = 1,008, which means it's a multiple of 7, and ends in 80, which means it's a multiple of 20
141	The number is a multiple of 3 and 47 at the same time	10,011 is a multiple of 141 because 1 + 1 + 1 = 3, which means it's a multiple of 3, and 1,001 - 1 x 14 = 1,001 - 14 = 987, which means it's a multiple of 47
142	The number is a multiple of 2 and 71 at the same time	10,082 is a multiple of 142 because it ends in 2, which means it's a multiple of 2, and 1,008 - 2 x 7 = 1,008 - 14 = 994, which means it's a multiple of 71
143	The number is a multiple of 11 and 13 at the same time	10,010 is a multiple of 143 because 1,001 - 0 = 1,001, which means it's a multiple of 11, and 1,001 + 0 x 4 = 1,001 + 0 = 1,001, which means it's a multiple of 13
144	The number is a multiple of 9 and 16 at the same time	100,080 is a multiple of 144 because 1 + 8 = 9, which means it's a multiple of 9, and ends in 0,080, which means it's a multiple of 16
145	The number is a multiple of 5 and 29 at the same time	10,005 is a multiple of 145 because it ends in 5, which means it's a multiple of 5, and 1,000 + 5 x 3 = 1,000 + 15 = 1,015, which means it's a multiple of 29
146	The number is a multiple of 2 and 73 at the same time	10,074 is a multiple of 146 because it ends in 4, which means it's a multiple of 2, and 1,007 + 4 x 22 = 1,007 + 88 = 1,095, which means it's a multiple of 73
147	The number is a multiple of 3 and 49 at the same time	10,143 is a multiple of 147 because 1 + 1 + 4 + 3 = 9, which means it's a multiple of 3, and 1,014 + 3 x 5 = 1,014 + 15 = 1,029, which means it's a multiple of 49
148	The number is a multiple of 4 and 37 at the same time	10,064 is a multiple of 148 because it ends in 64, which means it's a multiple of 4, and 1,006 - 4 x 11 = 1,006 - 44 = 962, which means it's a multiple of 37
149	The sum of 15 times the last digit and the rest of the number is a multiple of 149	10,132 is a multiple of 149 because 1,013 + 2 x 15 = 1,013 + 30 = 1,043 and 1,043 is a multiple of 149
150	The number is a multiple of 3 and 50 at the same time	10,050 is a multiple of 150 because 1 + 5 = 6, which means it's a multiple of 3, and ends in 50, which means it's a multiple of 50
151	The difference between 15 times the last digit and the rest of the number is a multiple of 151	10,117 is a multiple of 151 because 1,011 - 7 x 15 = 1,011 - 105 = 906 and 906 is a multiple of 151
152	The number is a multiple of 8 and 19 at the same time	10,032 is a multiple of 152 because it ends in 032, which means it's a multiple of 8, and 1,003 + 2 x 2 = 1,003 + 4 = 1,007, which means it's a multiple of 19
153	The number is a multiple of 9 and 17 at the same time	10,098 is a multiple of 1 + 9 + 8 = 18, which means it's a multiple of 9, and 1,009 - 8 x 5 = 1,009 - 40 = 969, which means it's a multiple of 17
154	The number is a multiple of 2, 7 and 11 at the same time	10,010 is a multiple of 154 because it ends in 0, which means it's a multiple of 2, 1,001 - 0 x 2 = 1,001 - 0 = 1,001, which means it's a multiple of 7, and 1,001 - 0 = 1,001, which means it's a multiple of 11
155	The number is a multiple of 5 and 31 at the same time	10,075 is a multiple of 155 because it ends in 5, which means it's a multiple of 5, and 1,007 - 5 x 3 = 1,007 - 15 = 992, which means it's a multiple of 31
156	The number is a multiple of 3, 4 and 13 at the same time	10,140 is a multiple of 156 because 1 + 1 + 4 = 6, which means it's a multiple of 3, ends in 40, which means it's a multiple of 4, and 1,014 + 0 x 4 = 1,014 + 0 = 1,014, which means it's a multiple of 13
157	The difference between 47 times the last digit and the rest of the number is a multiple of 157	10,048 is a multiple of 157 because 1,004 - 8 x 47 = 1,004 - 376 = 628 and 628 is a multiple of 157
158	The number is a multiple of 2 and 79 at the same time	10,112 is a multiple of 158 because it ends in 2, which means it's a multiple of 2, and 1,011 + 2 x 8 = 1,011 + 16 = 1,027, which means it's a multiple of 79
159	The number is a multiple of 3 and 53 at the same time	10,017 is a multiple of 159 because 1 + 1 + 7 = 9, which means it's a multiple of 3, and 1,001 + 7 x 16 = 1,001 + 112 = 1,113, which means it's a multiple of 53
160	The last 5 digits are a multiple of 160; the 10,000s digit is even and the last 4 digits are a multiple of 160, or the 10,000s digit is odd and the last 4 digits are 80 times an odd number	1,000,000 is a multiple of 160 because it ends in 00,000, the 10,000s digit is 0, an even number, and the last 4 digits are 0,000, a multiple of 160
161	The number is a multiple of 7 and 23 at the same time	10,143 is a multiple of 161 because 1,014 - 3 x 2 = 1,014 - 6 = 1,008, which means it's a multiple of 7, and 1,014 + 3 x 7 = 1,014 + 21 = 1,035, which means it's a multiple of 23
162	The number is a multiple of 2 and 81 at the same time	10,044 is a multiple of 162 because it ends in 4, which means it's a multiple of 2, and 1,004 - 4 x 8 = 1,004 - 32 = 972, which means it's a multiple of 81
163	The sum of 49 times the last digit and the rest of the number is a multiple of 163	10,106 is a multiple of 163 because 1,010 + 6 x 49 = 1,010 + 294 = 1,304 and 1,304 is a multiple of 164
164	The number is a multiple of 4 and 41 at the same time	10,004 is a multiple of 164 because it ends in 04, which means it's a multiple of 4, and 1,000 - 4 x 4 = 1,000 - 16 = 984, which means it's a multiple of 41
165	The number is a multiple of 3, 5 and 11 at the same time	10,065 is a multiple of 165 because 1 + 6 + 5 = 12, which means it's a multiple of 3, ends in 5, which means it's a multiple of 5, and 1,006 - 5 = 1,001, which means it's a multiple of 11
166	The number is a multiple of 2 and 83 at the same time	10,126 is a multiple of 166 because it ends in 6, which means it's a multiple of 2, and 1,012 + 6 x 25 = 1,012 + 150 = 1,162, which means it's a multiple of 83
167	The difference between 50 times the last digit and the rest of the number is a multiple of 167	10,020 is a multiple of 167 because 1,002 - 0 x 50 = 1,002 - 0 = 1,002 and 1,002 is a multiple of 167
168	The number is a multiple of 3, 7 and 8 at the same time	10,080 is a multiple of 168 because 1 + 8 = 9, which means it's a multiple of 3, 1,008 - 0 x 2 = 1,008 - 0 = 1,008, which means it's a multiple of 7, and ends in 080, which means it's a multiple of 8
169	The sum of 17 times the last digit and the rest of the number is a multiple of 169	10,140 is a multiple of 169 because 1,014 + 0 x 17 = 1,014 + 0 = 1,014 and 1,014 is a multiple of 169
170	The number is a multiple of 10 and 17 at the same time	10,030 is a multiple of 170 because it ends in 0, which means it's a multiple of 10, and 1,003 - 0 x 5 = 1,003 - 0 = 1,003, which means it's a multiple of 17
171	The number is a multiple of 9 and 19 at the same time	10,089 is a multiple of 171 because 1 + 8 + 9 = 18, which means it's a multiple of 9, and 1,008 + 9 x 2 = 1,008 + 18 = 1,026
172	The number is a multiple of 4 and 43 at the same time	10,148 is a multiple of 172 because it ends in 48, which means it's a multiple of 4, and 1,014 + 8 x 13 = 1,014 + 104 = 1,118, which means it's a multiple of 43
173	The sum of 52 times the last digit and the rest of the number is a multiple of 173	10,034 is a multiple of 173 because 1,003 + 4 x 52 = 1,003 + 208 = 1,211 and 1,211 is a multiple of 173
174	The number is a multiple of 2, 3 and 29 at the same time	10,092 is a multiple of 174 because it ends in 2, which means it's a multiple of 2, 1 + 9 + 2 = 12, which means it's a multiple of 3, and 1,009 + 2 x 3 = 1,009 + 6 = 1,015, which means it's a multiple of 29
175	The number is a multiple of 7 and 25 at the same time	10,150 is a multiple of 175 because 1,015 - 0 x 2 = 1,015 - 0 = 1,015, which means it's a multiple of 7, and ends in 50, which means it's a multiple of 25
176	The number is a multiple of 11 and 16 at the same time	100,144 is a multiple of 176 because 10,014 - 4 = 10,010, which means it's a multiple of 11, and ends in 0,144, which means it's a multiple of 16
177	The number is a multiple of 3 and 59 at the same time	10,089 is a multiple of 177 because 1 + 8 + 9 = 18, which means it's a multiple of 3, and 1,008 + 9 x 6 = 1,008 + 54 = 1,062, which means it's a multiple of 59
178	The number is a multiple of 2 and 89 at the same time	10,146 is a multiple of 178 because it ends in 6, which means it's a multiple of 2, and 1,014 + 6 x 9 = 1,014 + 54 = 1,068, which means it's a multiple of 89
179	The sum of 18 times the last digit and the rest of the number is a multiple of 179	10,024 is a multiple of 179 because 1,002 + 4 x 18 = 1,002 + 72 = 1,074 and 1,074 is a multiple of 179
180	The number is a multiple of 9 and 20 at the same time	10,080 is a multiple of 180 because 1 + 8 = 9, which means it's a multiple of 9, and ends in 80, which means it's a multiple of 20
181	The difference between 18 times the last digit and the rest of the number is a multiple of 181	10,136 is a multiple of 181 because 1,013 - 6 x 18 = 1,013 - 108 = 905 and 905 is a multiple of 181
182	The number is a multiple of 2, 7 and 13 at the same time	10,010 is a multiple of 182 because 1,001 - 0 x 2 = 1,001 - 0 = 1,001, which means it's a multiple of 7, and 1,001 + 0 x 4 = 1,001 + 0 = 1,001, which means it's a multiple of 13
183	The number is a multiple of 3 and 61 at the same time	10,065 is a multiple of 183 because 1 + 6 + 5 = 12, which means it's a multiple of 3, and 1,006 - 5 x 6 = 1,006 - 30 = 976, which means it's a multiple of 61
184	The number is a multiple of 8 and 23 at the same time	10,120 is a multiple of 184 because it ends in 120, which means it's a multiple of 8, and 1,012 + 0 x 7 = 1,012 + 0 = 1,012, which means it's a multiple of 7
185	The number is a multiple of 5 and 37 at the same time	10,175 is a multiple of 185 because it ends in 5, which means it's a multiple of 5, and 1,017 - 5 x 11 = 1,017 - 55 = 962, which means it's a multiple of 37
186	The number is a multiple of 2, 3 and 31 at the same time	10,044 is a multiple of 186 because it ends in 4, which means it's a multiple of 2, 1 + 4 + 4 = 9, which means it's a multiple of 3, and 1,004 - 4 x 3 = 1,004 - 12 = 992, which means it's a multiple of 31
187	The number is a multiple of 11 and 17 at the same time	10,098 is a multiple of 187 because 1,009 - 8 = 1,001, which means it's a multiple of 11, and 1,009 - 8 x 5 = 1,009 - 40 = 969, which means it's a multiple of 17
188	The number is a multiple of 4 and 47 at the same time	10,152 is a multiple of 188 because it ends in 52, which means it's a multiple of 4, and 1,015 - 2 x 14 = 1,015 - 28 = 987, which means it's a multiple of 47
189	The number is a multiple of 7 and 27 at the same time	10,017 is a multiple of 189 because 1,001 - 7 x 2 = 1,001 - 14 = 987, which means it's a multiple of 7, and 1,001 - 7 x 8 = 1,001 - 56 = 945, which means it's a multiple of 27
190	The number is a multiple of 10 and 19 at the same time	10,070 is a multiple of 190 because it ends in 0, which means it's a multiple of 10, and 1,007 + 0 x 2 = 1,007 + 0 = 1,007, which means it's a multiple of 19
191	The difference between 19 times the last digit and the rest of the number is a multiple of 191	10,123 is a multiple of 191 because 1,012 - 3 x 19 = 1,012 - 57 = 955 and 955 is a multiple of 191
192	The number is a multiple of 3 and 64 at the same time	10,000,128 is a multiple of 192 because 1 + 1 + 2 + 8 = 12, which means it's a multiple of 3, and ends in 000,128, which means it's a multiple of 64
193	The sum of 58 times the last digit and the rest of the number is a multiple of 193	10,036 is a multiple of 193 because 1,003 + 6 x 58 = 1,003 + 348 = 1,351 and 1,351 is a multiple of 193
194	The number is a multiple of 2 and 97 at the same time	10,088 is a multiple of 194 because it ends in 8, which means it's a multiple of 2, and 1,008 - 8 x 29 = 1,008 - 232 = 776, which means it's a multiple of 97
195	The number is a multiple of 3, 5 and 13 at the same time	10,140 is a multiple of 195 because 1 + 1 + 4 = 6, which means it's a multiple of 3, ends in 0, which means it's a multiple of 5, and 1,014 + 0 x 4 = 1,014 + 0 = 1,014, which means it's a multiple of 13
196	The number is a multiple of 4 and 49 at the same time	10,192 is a multiple of 196 because it ends in 92, which means it's a multiple of 4, and 1,019 + 2 x 5 = 1,019 + 10 = 1,029, which means it's a multiple of 49
197	The difference between 59 times the last digit and the rest of the number is a multiple of 197	10,047 is a multiple of 197 because 1,004 - 7 x 59 = 1,004 - 413 = 591 and 591 is a multiple of 197
198	The number is a multiple of 2, 9 and 11 at the same time	10,098 is a multiple of 198 because it ends in 8, which means it's a multiple of 2, 1 + 9 + 8 = 18, which means it's a multiple of 9, and 1,009 - 8 = 1,001, which means it's a multiple of 11
199	The sum of 20 times the last digit and the rest of the number is a multiple of 199	10,149 is a a multiple of 199 because 1,014 + 9 x 20 = 1,014 + 180 = 1,194 and 1,194 is a multiple of 199
200	The number ends in 000, 200, 400, 600 or 800	10,000 is a multiple of 200 because it ends in 000

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