# Divisibility Rule

## Divisibility Rule

Rule that helps to determine if a number is divisible by another number without needing to carry out the division.

The properties of a number that allow us to determine if this number is divisible by another number are properties that characterize this divisibility. Because these are also conditions of divisibility, we also talk about “divisibility criteria”.

### Properties

Here are a few divisibility rules.

A number is divisible :

• by 2 if its last digit represents an even number: 24, 32 and 64 are divisible by 2.
• by 3 if its digital sum is divisible by 3: 36, 24 and 237 are divisible by 3.
• by 4 if it is divisible by 2 two times successively or if the number formed by its last two digits is divisible by 4: 24, 248 and 564 are divisible by 4.
• by 5 if its last digit is 0 or 5: 50, 65 and 125 are divisible by 5.
• by 6 if it is an even number with a digital sum that is divisible by 3: 72, 132 and 468 are divisible by 6.
• by 7 if the difference (in absolute value) between its tens digit and the double of its ones digit is divisible by 7. Repeat this process until you get a result that is less than 14. The final result is 0, 7 or 14: 84, 105 and 420 are divisible by 7.
• by 8 if it is divisible by 2 three times in a row or if the number formed by its last three digits is divisible by 8: 192, 576 and 1728 are divisible by 8.
• by 9 if its digital sum is divisible by 9: 99, 693 and 2772 are divisible by 9.
• by 10 if its last digit is 0: 50, 260 and 1300 are divisible by 10.
• by 11 if the difference between the digital sum of the digits in the odd positions and the digital sum of the digits in the even positions is divisible by 11: 33, 154 and 1386 are divisible by 11.
• by 12 if it is divisible by both 4 and 3: 48, 432 and 2160 are divisible by 12.
• by 100 if its last two digits are 0: 300, 1600 and 200 are divisible by 100.