Test for Divisibility

2

all EVEN numbers (numbers ending in 0,2,4,6, & 8) are divisible by 2 ex. 4,832 (even) is divisible by 2. 4,831 (odd) is not divisible by 2.

6

any even number divisible by 3 is divisible by 6. ex. the sum of the digits of 2,778 is 24, which is divisible by 3. so 2,778 is an even number divisible by 3, which means it is divisible by 6.

3

if the SUM of the digits of a number is divisible by 3, then the number is divisible by 3. ex. the sum of the digits of 6,711 is 15, which is divisible by 3. so 6,711 is divisible by 3

8

if the last three digits of a number are divisible by 8, then the number is divisible by 8. ex. the last three digits of 103,488 are 488, which is divisible by 8. so 103,488 is divisible by 8.

4

if the last two digits of a number are divisible by 4, then the number is divisible by four. ex. the last two digits of 4,776 are 76, which is divisible by four. so 4,776 is divisible by four.

9

if the sum of the digits of a number is divisible by 9, then the number is divisible by 9. ex. the sum of the digits of 8,343 is 18, which is divisible by 9. so 8,343 is divisible by 9.

11

remove the last digit and subtract it from the remaining truncated number. repeat until what remains is either divisible by 11 or not. consider 8,173. 817 - 3 = 814; 81 - 4 = 77, which is divisible by 11. so 8,173 is divisible by 11.

7

remove the last digit, double it, and then subtract it from the truncated original number. repeat until what remains is either divisible by 7 or not. ex. consider 3,248. 324 - 16 = 308; 30 - 16 = 14, which is divisible by 7. so 3,248 is divisible by 7.

13

remove the last number, multiply it by 4, and then add it to the remaining truncated number. repeat until what remains is divisible by 13 or not. ex. consider 18,902. 1,890 + 8 = 1,898; 189 + 32 = 221; 22 + 4 = 26, which is divisible by 13. so 18,902 is divisible by 13.

12

any number divisible by 3 and 4 is also divisible by 12. ex. consider 38,424. the sum of the digits is 21, which is divisible by 3 the last two digits are 24, which is divisible by 4. so 38,424 is divisible by 3 & 4, which means it is divisible by 12.

10

any number ending in 0 is divisible by 10. ex. 450, 9,230, and 107,770 are divisible by 10.

5

any number ending in 0 or 5 is divisible by 5. ex. 3,745 and 2,670 are divisible by 5.