Divisibility rules are a set of mathematical tricks that can help you quickly determine whether a given number is divisible by another number without having to perform long divisions. These rules are based on the observation that certain numbers have distinct patterns of digits that repeat when multiplied by another number.

We will explore some of the most common divisibility rules that can make your life easier when working with numbers.

**Divisibility by 2, 4, and 8**:

A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).

*8,356 is divisible by 2 because the last digit is 6.*

A number is divisible by 4 if the last two digits are divisible by 4.

*12,648 is divisible by 4 because the last two digits (48) are divisible by 4.*

A number is divisible by 8 if the last three digits are divisible by 8.

*79,312 is divisible by 8 because the last three digits (312) are divisible by 8.*

**Divisibility by 3 and 9:**

A number is divisible by 3 if the sum of its digits is divisible by 3.

*2,478 is divisible by 3 because the sum of its digits (2+4+7+8) is 21, which is divisible by 3.*

A number is divisible by 9 if the sum of its digits is divisible by 9.

*8,643 is divisible by 9 because the sum of its digits (8+6+4+3) is 21, which is divisible by 9*.

**Divisibility by 5 and 10:**

A number is divisible by 5 if the last digit is either 0 or 5.

*45,650 is divisible by 5 because the last digit is 0.*

A number is divisible by 10 if the last digit is 0.

*4,536,320 is divisible by 10 because the last digit is 0.*

**Divisibility by 6:**

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

*2,934 is divisible by 6 because it is divisible by 2 (last digit is 4) and by 3 (sum of its digits is 18, which is divisible by 3).*

Knowing these divisibility rules can save you a lot of time and effort when working with numbers. You can use them to quickly determine whether a number is divisible by another number, which can be especially useful when you are working with large numbers. Practice using these rules and you will soon find that doing mental arithmetic is much easier and more enjoyable. Be sure to save the graphic below!

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