Need to divide whole numbers quickly? Follow these 4 divisibility rules ➗

Your teacher places several number cards on the table and says, “Today we’re testing your number sense.” Each card has a large number on it, and your job is to decide if the numbers can be divided evenly.

Then comes the challenge: 10 numbers in 3 minutes — no calculator! Some numbers are large, and you know that long division would take too long.

You're worried at first! But then you remember that mathematicians discovered patterns called divisibility rules that act like quick clues. These shortcuts can help you quickly tell whether a number can be divided evenly — no long division needed!

Divisibility rules help you determine whether one number can be divided evenly by another number without actually having to divide the numbers. You can determine this just by examining the digits in a number!

Learning divisibility rules can save you time when dividing, simplifying fractions, factoring numbers, or finding prime and composite numbers. They can help you find the answer quickly.

The numbers 2, 4, and 8 are all even numbers, meaning they can be shared equally. They share the same factor too — the number 2!

• 2 x 1 = 2

• 2 x 2 = 4, and

• 2 x 4 = 8

To test whether a number is divisible by either of these, look at the last digit.

A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). Suppose you have the number 159,346. Look at the last digit — 6. It's divisible by 2:

• 2 x 3 = 6

So, 159,346 is divisible by 2. You get 75,673.

Check the last two digits of a number to determine if it's divisible by 4. If they're divisible by 4, then your number is divisible by four.

Say you have 7,816. Is it divisible by 4? Check the last two digits — 16. 16 is divisible by 4:

• 4 x 4 = 16

So 7,816 is divisible by 4. You get 1,954.

Numbers are divisible by 8 when the last three digits are divisible by 8, or when you can divide a number three times by 2 and have no remainder.

Let's see how that works. Suppose you have 143,128.

Strategy #1

Look at the last three digits: 128. Are they divisible by 8?

Since 16 x 8 = 128, 143,128 is divisible by 8. You'll get 17,891.

Strategy #2

Try dividing this number by 2, 3 times, which might be a bit easier!

143,128 divided by 2 is 71,564. Divide 71,564 by 2, and you get 35,782. Divide by 2 again, and you get 17,891.

The number 5 is a prime number, meaning that the only factors that multiply together to equal 5 are 1 and 5 (1 x 5 = 5).

A number is divisible by 5 if it ends in either 5 or 0. For example, 825 is divisible by 5 because it ends in five (165 x 5 = 825). The number 9,000 is also divisible by 5 because it ends in 0 (1,800 x 5 = 9,000).

Take the number 45,610. This number ends with zero and is therefore divisible by 5 (9,122 x 5 = 45,610).

The numbers 3, 6, and 9 all have something in common...the number 3! Each number has 3 as its factor

• 3 x 1 = 3

• 3 x 2 = 6

• 3 x 3 = 9

These numbers are connected in terms of divisibility, too!

A number is divisible by 3 if the sum of its digits is divisible by 3. Take a look at the number 372. If you add up these digits (3 + 7 + 2), you get 12, which is divisible by 3.

Tip! If you didn't know that 12 was divisible by 3, you could add 1 + 2 together to get 3, which is divisible by 3.

For a number to be divisible by 6, it must be divisible by both 2 and 3. This means the number must be even to be divisible by 2.

Take the number 138. It is an even number because the last digit is even (0, 2, 4, 6, 8). But, is it divisible by 3? Add the digits to find out! 1 + 3 + 8 = 12... add again 1 + 2 = 3... YES! It is divisible by three! Therefore, it's divisible by 6 (23 x 6 = 138)!

What about 9? If the sum of all the digits is divisible by 9, then the number is divisible by 9.

Take 1,008, for example. Add the digits (1 + 0 + 0 + 8), which equals 9. 9 is divisible by 9. How about 444,123? Add up the digits (4 + 4 + 4 + 1 + 2 + 3) to get 18. Add again (1 + 8) to get 9. YES! It's divisible by nine!

Photo by Eric Prouzet on Unsplash

The number 7 is a tricky number when it comes to divisibility rules. It has a rule all its own! You'll have to perform a few steps to find whether a number is divisible by 7.

Perform these steps:

1. Double the last digit

2. Then subtract it from the remaining part of the number.

3. If the result is 0 (zero) or a multiple of 7, the original number is divisible by 7; if not, repeat steps 1 and 2.

Example: Is 1,071 divisible by 7?

1. Double the last digit. 1 doubled is 2.

2. Subtract 2 from the remaining part of the number. 107 (remaining part) - 2 = 105

3. Since 105 doesn't end in 0 or a multiple of 7, repeat steps 1 and 2.

4. Double the last digit. 5 doubled is 10.

5. Subtract 10 from the remaining part of the number. 10 (remaining part) - 10 = 0

Since the result ends in 0, the number 1,071 is divisible by 7 (153 x 7 = 1,071)!

Alright! Now that you have some divisibility rules under your belt, go divide and conquer! No, seriously...go try these rules out on some numbers! And, if you need additional help, these resources might be just what you need: