Arithmetic - Divisibility Rules

Question 1

dividing by 2

Answer 1

last digit is even

Question 2

dividing by 3

Answer 2

the sum of the digits is divisible by 3

Example: 3 + 8 + 1 = 12 and 12 / 3 = 4

Question 3

dividing by 4

Answer 3

the last two digits of the number are divisible by 4

Example: 1312 and 12 / 4 =3

Question 4

dividing by 5

Answer 4

if the last digit is a 5 or a 0, then the number is divisible by 5

Question 5

dividing by 6

Answer 5

if the number is divisible by both 3 and 2, it is divisible by 6

Question 6

dividing by 7

Answer 6

take the last digit, double it, and subtract it from the remaining digits, if the answer is 0 or 7 it is divisible by 7

you can apply this rule to the answer again

Example:
2016
6 x 2 = 12
201 - 12 = 189
9 x 2 = 18
18 - 18 = 0

Question 7

dividing by 8

Answer 7

the last three digits are divisible by 8
Example: 109816
816 / 8 = 102

Question 8

dividing by 9

Answer 8

if the sum of the digits is divisible by 9
Example: 12348
1 + 2 + 3 + 4 + 8 = 18
18 / 9 = 2

Question 9

dividing by 10

Answer 9

if the number ends in 0

Question 10

dividing by 11

Answer 10

if you sum every second digit and then subtract all other digits and the answer is 0 or divisible by 11
Example: 1364
1 + 6 = 7
3 + 4 = 7
7 - 7 =0

Question 11

dividing by 12

Answer 11

if the number is divisible by both 3 and 4

Question 12

dividing by 13

Answer 12

-delete the last digit from the given number
-subtract nine times the deleted digit from the remaining digits
-if what is left is divisible by 13 then so is the original
-Example: 104
4 x 9 = 36
10 - 36 = -26
-26 / 13 =-2