**Divisibility rules** are useful for quickly determining if a number is divisible by a particular factor without having to perform long division. This can be especially helpful for large numbers or when mental calculation is required.

Here are some reasons why divisibility rules are important:

**Efficiency:**Divisibility rules provide a shortcut for determining divisibility, saving time and effort compared to performing long division.**Mental calculation:**Divisibility rules can be applied mentally, allowing for quick and easy calculations without the need for a calculator or other tools.**Pattern recognition:**Divisibility rules help identify patterns in numbers, making it easier to spot multiples of a particular factor.**Problem-solving:**Divisibility rules can be used to solve problems related to divisibility, such as finding the greatest common factor (GCF) or least common multiple (LCM) of two or more numbers.**Number theory:**Divisibility rules play a fundamental role in number theory, a branch of mathematics that deals with the properties of integers.

We begin with** 1**, which all numbers are divisible by.

3420 **÷** 1 = 3420

**Divisible by 2** If the number is even or ends in 0 it is divisible by 2.

234 **÷ 2 = 117**

230 **÷ 2 = 115**

**Divisible by 3.** If the sum of the Digits is divisible by three the entire number is divisible by 3.

See the short video for an example.

** Divisible by 4.** If the last two digits are divisible by 4 then the entire number is divisible by 4.

Check out the short video for an example problem.

** Divisible by 5.** If the number ends in 5 or 0 then the number is divisible by 5

375 **÷ 5 = 75**

4520 **÷ 5 = 904**

**Divisible by 6**. If the number is even and divisible by 3, then the entire number is divisible by 6.

384

It is even and …

The sum of the digits is divisible by 3

3+8+4 = 15 **÷3 = 5**

so 384 is divisible by 6.

**Divisible by 7:**Double the last digit, subtract from the remaining digits. If the result is divisible by 7 or 0, so is the original number.

Check out the short video for an example problem.

**Divisible by 8: **Last three digits are divisible by 8

Is 45216 divisible by 8?

Last three digits 216 are divisible by 8

216 ÷ 8 = 27 so the entire number is divisible by 8.

**Divisible by 9: **Sum of the digits is divisible by 9

Check out the short video for an example problem.

**Divisible by 10: **Ends in 0

456780 ÷ 10 = 45,678