The following set of rules can help you save time in trying to check the divisibility of numbers.
A number is divisible by

if

2

it ends in 0, 2, 4, 6, or 8

3

the sum of its digits is divisible by 3

4

the number formed by the last two digits is divisible by 4

5

it ends in 0 or 5

6

it is divisible by 2 and 3 (use the rules for both)

7

(no simple rule)

8

the number formed by the last three digits is divisible by 8

9

the sum of its digits is divisible by 9

Example 1

Is 126 divisible by 3? Sum of digits = 9. Because 9 is divisible by 3, then 126 is divisible by 3.

Is 1,648 divisible by 4? Because 48 is divisible by 4, then 1,648 is divisible by 4.

Is 186 divisible by 6? Because 186 ends in 6, it is divisible by 2. Sum of digits = 15. Because 15 is divisible by 3, 186 is divisible by 3. 186 is divisible by 2 and 3; therefore, it is divisible by 6.

Is 2,488 divisible by 8? Because 488 is divisible by 8, then 2,488 is divisible by 8.

Is 2,853 divisible by 9? Sum of digits = 18. Because 18 is divisible by 9, then 2,853 is divisible by 9.