1. the first number is divisible by the second number and
2. the second number divides the first.
Example 1: 9 divided by 3
Since the remainder is 0, then 9 is divisible by 3.
Example 2: Is 21 divisible by 4?
Since the remainder is not 0, then 21 is not divisible by 4.
Divisibility Rules
Here are some rules to follow if a number is exactly divisible by 2, 3, 4, 5, 6, 8, 9, 10 and 11. Try remembering them!
1. Divisibility by 2
Even numbers with units digit of 0, 2, 4, 6, or 8 are divisible by 2.
Example: 44, 90, 136, 81 632
2. Divisibility by 3
A number is divisible by 3 if the sum of the digits of the number is divisible by 3.
Example: 15, 24, 30
1 + 5 = 6 , 6 is divisible by 3, so 15 is divisible by 3
2 + 4 = 6
3 + 0 = 3
3. Divisibility by 4
If the last two digits of a number form a number that is divisible by 4, then the number is divisible by 4. Likewise, if the last two digits of a number is 00, then it is considered as divisible by 4.
Example: 612, 900, 3 064
612 , 12 is divisible by 4, so 612 is divisible by 4
900 , 00 is divisible by 4
3 064 , 64 is divisible by 4
If a number is divisible by 4 then it is also divisible by 2.
4. Divisibility by 5
If the last digit of a number is 0 or 5, then the number is divisible by 5.
Example: 300, 775, 825
5. Divisibility by 6
If a number is divisible by both 2 and 3 then it is divisible by 6. Or, if any even number is divisible by 3 then it is divisible by 6.
Example: 720 can be divided by 2 or 3 without any remainder then it is also divisible by 6. It is also an even number.
But is 1 453 divisible by 6?
6. Divisibility by 8
A number is divisible by 8 if the number in the last 3 digits is divisible by 8.
Example: 1664 is divisible by 8 since 664 can be divided by 8 without remainder.
7. Divisibility by 9
A number is divisible by 9 if the sum of the digits is divisible by 9.
Example: 42, 570 --> 4 + 2 + 5 + 7 + 0 = 18 and 18 is divisible by 9.
8. Divisibility by 10
A number is divisible by 10 if the last digit or units or the ones is zero, 0.
Example: 420, 6 110, 298 730
9. Divisibility by 11
A number is divisible by 11 if the difference between the sums of the digits in the odd places and the digits in the even places is either 0 or a multiple of 11.
Example:
2 642 805
Odd numbers: 5 + 8 + 4 + 2 = 19
Even numbers: 0 + 2 + 6 = 8
19 - 8 = 11
A multiple of 11!
