Divisibility Rules

A number is divisible by another number if it divides evenly without a remainder.

For example, 8 is divisible by 4 since 8 ÷ 4 = 2 R0.

The following divisibility rules apply to whole numbers.

Divisor Divisibility Rule Example Non - Example 2 Any whole number that ends in 78558 is divisible by 78559 is not 0, 2, 4, 6, or 8 is divisible by 2. 2 since the last digit divisible by since is 8. the last digit is 9. (i.e. Any even number is divisible by 2). 3 If the sum of the digits is 1539 is divisible by 1540 is not divisible by 3, than the whole 3 since 1 + 5 + 3 + 9 divisible by 3 since number is also divisible by 3. = 18 and 18 is 1 + 5 + 4 + 0 = 10 divisible by 3. and 10 is not divisible by 3. 4 If the last two digits of the 19236 is divisible by 19237 is not whole number form a two-digit 4 since the last two divisible by 4 since number that is divisible by 4, digits, 36, form a the last two digits, than the whole number is also number that is 37, form a number divisible by 4. divisible by 4. that is not divisible by 4. 5 Any whole number that ends in 87235 is divisible by 87234 is not 0 or 5 is divisible by 5. 5 since the number divisible by 5 since ends in 5. the number ends in 4. 6 If a whole number is divisible 5622 is divisible by 5630 is not by 2 AND 3, than it is divisible 6 since this number divisible by 6 since by 6. is divisible by 2 (it the number is ends in 2) and by 3 divisible by 2 (it (5+6+2+2=15 and ends in 0) but not 15 is divisible by 3). by 3 (5+6+3+0=14 and 14 is not divisible by 3). 8 If the last three digits of the 78160 is divisible by 78161 is not whole number form a three- 8 since the last divisible by 8 since digit number that is divisible three digits, 160, the last three

by 8, than the whole number is form a number that digits, 161, form a also divisible by 8. is divisible by 8 (160 number that is not ÷ 8 = 20). divisible by 8. 9 If the sum of the digits is 178245 is divisible 178243 is not divisible by 9, than the whole by 9 since divisible by 9 since number is also divisible by 9. 1+7+8+2+4+5=27 1+7+8+2+4+3=25 and 27 is divisible and 25 is not by 9 (27 ÷ 9 = 3) divisible by 9 10 Any whole number that ends in 149830 is divisible 149835 is not 0 is divisible by 10. by 10 since it ends divisible by 10 in 0. since it ends in 5.

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