## Rules of Divisibility

The following is a list of divisibility rules for the numbers 1-13, 17, and 19. For some numbers, other ways have been included to check for divisibility. (Things that make you go hmmm?!?)

**Divisibility by 1:**

*Any number divided by one is equal to itself: 3/1 = 3, 5/1 = 5*

**Divisibility by 2:**

*All numbers ending in 0,2,4,6,8 are divisible by 2.*

54278 is even since it ends in an even number, therefore is divisible by 2.

**Divisibility by 3:**

*If the sum of the digits is divisible by 3 then so is the original number.*

Is 5136 divisible by 3? Let�s check: 5 + 1 + 3 + 6 = 15. Since 15 is divisible by three then 5136 is divisible by 3.

**Divisibility by 4:**

*If the last two digits are divisible by 4 then so is the original number.*

Is 87532 divisible by 4? Let�s check: 32/4 = 8. Since 32 is divisible by 4 then 87532 is divisible by 4.

**Divisibility by 5:**

*If the number ends in 0 or 5 then it is divisible by 5.*

Is 345,740 divisible by 5? Let�s check: Since 345,740 ends in 0 then it is divisible by 5.

Is 560,985 divisible by 5? Let�s check: Since 560,985 ends in 5 then it is divisible by 5.

**Divisibility by 6:**

*If a number is divisible by 2 and 3, then it is divisible by 6.*

Is 5964 divisible by 6? Let�s check: Since 5964 is an even number and 5 + 9 + 6 + 4 = 24, which is divisible by 3, then 5964 is divisible by 6.

Is 670 divisible by 6? Let�s check: 670 is an even number, but 6 + 7 + 0 = 13 which is not divisible by 3, therefore 670 is not divisible by 6.

**Divisibility by 7:**

*If a number is divisible by 7, take the last digit, double it, and subtract it from the rest of the number. If the result is divisible by 7 then the original number is divisible by 7.*

Is 217 divisible by 7? Let�s check: 7*2 = 14. 21-14 = 7. Since 7 is divisible by 7 then 217 is also.

Is 896 divisible by 7? Let�s check: 6*2 = 12. 89-12 = 77. Since 77 is divisible by 7 then 896 is also.

**Divisibility by 8:**

*If the last three digits are divisible by 8, then the original number is divisible by 8. How do you know if the last three digits are divisible by 8? If the last two digits are divisible by eight and the first digit is even, the number is divisible by 8. When the first digit is odd, subtract 4 from the last two digits and if the result is divisible by 8 then so is the original number.*

Let�s try two examples:

- 34,856: last three digits 856. Since 56 is divisible by 8 and the first digit, 8, is even, then 34,856 is divisible by 8.
- 980,744: last three digits 744. Since the first digit is odd we subtract 4 from 44. 44 - 4 = 40. Because 40 is divisible by eight, then 980,744 is also.

**Divisibility by 9:**

*If the sum of the digits is divisible by 9 then so is the original number.*

Is 675 divisible by 9? Let�s check: 6 + 7 + 5 = 18. Since 18 is divisible by 9, then so is 675.

**Divisibility by 10:**

*If a number ends in 0, then the number is divisible by 10.*

Is 5430 divisible by 10? Let�s check: Since 5430 ends in 10, it is divisible by 10.