Divisibility Rules

A number is divisible by another number if the division is exact.


Divisible by 2

A number is divisible by 2, if its last digit is a zero or an even number.

64, 278, 1,094.

Divisible by 3

A number is divisible by 3, if the sum of its digits 3 or is a multiple of 3.

12

1 + 2 = 3

564

5 + 6 + 4 = 15, is multiple 3

2,040

2 + 0 + 4 + 0 = 6, is multiple 3

Divisible by 4

A number is divisible by 4, if the last two digits are zeros or a multiple of 4.

16, 600, 1,028.

Divisible by 5

A number is divisible by 5, if it ends in zero or five.

15, 715, 7,725.

Divisible by 6

A number is divisible by 6, if it is divisible by 2 and 3.

42, 324, 60,012

Divisible by 7

A number is divisible by 7, when the difference between the number without the figure of the units and the double the number of the units is 0 or a multiple of 7.

343

34 − 2 · 3 = 28, is multiple of 7.

105

10 − 5 · 2 = 0

2261

226 − 1 · 2 = 224.

Repeat the process with 224.

22 − 4 · 2 = 14, is multiple of 7.

Divisible by 8

A number is divisible by 8, if its last three figures are zeros or a multiple of 8.

2,000, 5,048, 7,512.

Divisible by 9

A number is divisible by 9, if the sum of its digits gives a multiple of 9.

63

6 + 3 = 9

3,663

3 + 6 + 6 + 3 = 18, is multiple of 9

Divisible by 10

A number is divisible by 10, if the last figure in the unit is 0.

230, 5,440, 70,230

Divisible of 11

A number is divisible by 11, if the difference between the sum of the figures who occupy the even numbers and the odd numbers is 0 or a multiple of 11.

121

(1 + 1) − 2 = 0

4,224

(4 + 2) − (2+4) = 0

Divisible by 25

A number is divisible by 25, if their last two digits are zeros or a multiple of 25.

700, 6,025, 8,875.

Divisible by 125

A number is divisible by 125, if its last three figures are zeros or a multiple of 125.

3,000, 5,125, 7,250.





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