Divisibility Quick Kit: 18 flashcards

A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).

A number is divisible by 3 if the sum of its digits is divisible by 3. For 12345, sum = 1+2+3+4+5 = 15, and 15 is divisible by 3, so 12345 is divisible by 3.

A number is divisible by 4 if the number formed by its last two digits is divisible by 4. For 1232, last two digits are 32, and 32 ÷ 4 = 8, so 1232 is divisible by 4.

A number is divisible by 5 if its last digit is 0 or 5. Example: 125 is divisible by 5 because its last digit is 5.

A number is divisible by 6 if it is divisible by both 2 and 3. 234 ends in 4 (even) and sum of digits = 2+3+4 = 9 (divisible by 3), so 234 is divisible by 6.

A number is divisible by 8 if the number formed by its last three digits is divisible by 8. For 5312, last three digits are 312, and 312 ÷ 8 = 39, so 5312 is divisible by 8.

A number is divisible by 9 if the sum of its digits is divisible by 9. For 9873, sum = 9+8+7+3 = 27, and 27 is divisible by 9, so 9873 is divisible by 9.

A number is divisible by 10 if its last digit is 0. Example: 450 is divisible by 10 because it ends with 0.

A number is divisible by 11 if the difference between the sum of digits in alternating positions is 0 or a multiple of 11. For 121, (1+1) - 2 = 0, so 121 is divisible by 11.

A number is divisible by 12 if it is divisible by both 3 and 4. 144: sum of digits = 9 (divisible by 3) and last two digits 44 (divisible by 4), so 144 is divisible by 12.

A number is divisible by 15 if it is divisible by both 3 and 5. 225: sum of digits = 9 (divisible by 3) and last digit is 5 (divisible by 5), so 225 is divisible by 15.

There is no simple rule; one method is to double the last digit and subtract from the rest. For 343: 34 - 2*3 = 28, which is divisible by 7, so 343 is divisible by 7.

A number is divisible by 25 if its last two digits are 00, 25, 50, or 75. For 375, last two digits are 75, so it is divisible by 25.

A number is divisible by 18 if it is divisible by both 2 and 9. 198: last digit 8 (even) and sum of digits = 1+9+8 = 18 (divisible by 9), so 198 is divisible by 18.

A number is divisible by 20 if its last two digits are 00, 20, 40, 60, or 80. For 340, last two digits are 40, so it is divisible by 20.

A number is divisible by 36 if it is divisible by both 4 and 9. 720: last two digits 20 (divisible by 4) and sum of digits = 7+2+0 = 9 (divisible by 9), so 720 is divisible by 36.

A number is divisible by 45 if it is divisible by both 5 and 9. 135: last digit 5 (divisible by 5) and sum of digits = 1+3+5 = 9 (divisible by 9), so 135 is divisible by 45.

A number is divisible by 11 if the difference between the sum of digits in alternating positions is 0 or a multiple of 11. For 1331: (1+3) - (3+1) = 0, so 1331 is divisible by 11.