Simple Divisibility Tests 1 to 10

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There are some simple divisibility tests you can use to check if a number is divisible by the numbers 1 through 10.

It starts super simple.

Divisible by 1

Any number that divides by 1 is divisible by 1. Pretty obvious.

Divisible by 2

Any number that ends with the digits 2, 4, 6, 8 or 0 is divisible by 2.
Essentially any even number. For example: 12, 24, 26, 88, 100

Divisible by 3

A number is divisible by 3 if the sum of the digits of the number is divisible by 3.
For example, is 4325 divisible by 3?
Add the digits 4 + 3 + 2 + 5 = 14
14 is clearly not divisible by 3 (we can even use the same rule to check: 1 + 4 = 5, which is not divisible by 3!)
Is 654 divisible by 3?
6 + 5 + 4 = 15, which is divisible by 3, so yes! (just to confirm the rule, 1 + 5 = 6, which is definitely divisible by 3)

Divisible by 4

A number is divisible by 4 is the last 2 digits are divisible by 4.
For example, is 5469428 divisible by 4?
That’s a huge number, but we just have to look at the last 2 digits, 28.
Since 28 / 4 = 7, 5469428 is divisible by 4.
Consider 8826, is that divisible by 4?
Looking at the last 2 digits, 26, we see 26 / 4 = 6.5, so 8826 is not divisible by 4.

Divisible by 5

This is another simple one, any number ending in 0 or 5 is divisible by 5.
So 10, 105, 12345, 267548760, etc., all divisible by 5.

Divisible by 6

A number is divisible by 6 if it is divisible by 2 AND 3.
So basically we have to apply both of the earlier strategies.
For example, is 444 divisible by 6?
The last digit is a 4, and it’s even, so it’s divisible by 2.
Next, 4 + 4 + 4 = 12, since 12 is divisible by 3, 444 is divisible by 3.
Since 444 is divisible by 2 and 3, it’s divisible by 6.

If we add another 4, and get 4444, it’s still divisible by 2, but 4 + 4 + 4 + 4 = 16, which is not divisible by 3.
Therefore, 4444 is not divisible by 6.

You can try another example, 12345678 (it’s not divisible by 6, check it yourself!)

Divisible by 7

This one is a little tricky.
First we take the number’s last digit and multiply by 2.
Then subtract this result from the remaining number.
If the difference is divisible by 7, then the number is divisible by 7.
The problem is that if the number is too big for you to easily tell if the difference is divisible by 7, you may need to repeat this several times.

For example, is 5291 divisible by 7?
The last digit is 1, which we double to 2.
With the last digit removed, the number is now 529.
529 – 2 = 527
It’s not really obvious if 527 is divisible by 7, so we do this again.
The last digit is 7, double it to 14
The remaining number is 52
52 – 14 = 38, which is a manageable number
We know 38 doesn’t divide cleanly by 7, so we know 5291 is not divisible by 7

Let’s try another example: 54320
Last digit it 0, so we double it and subtract it from the remaining number, which gives us 5432 – (2 * 0) = 5432
We do it again, last digit 2, double it, subtract: 543 – (2 * 2) = 539
Once again, last digit 9, so 54 – (2 * 9) = 54 – 18 = 35
We know 35 / 7 = 5, therefore we know that 54320 is divisible by 7

If you want to practice, show that 687239 is divisible by 7

Divisible by 8

For a number to be divisible by 8, the last 3 digits need to be divisible by 8.
For example: 2347240
The last 3 digits are 240
Since 240 / 8 = 30, 2347240 is divisible by 8
It’s not always so clear that a 3 digit number is divisible by 8, but it is much easier to check using long division or some other method, especially when dealing with huge numbers.

For practice, show that 9329108 is not divisible by 8

Divisible by 9

A number is divisible by 9 if the sum of the digits is divisible by 9. Pretty similar to the method for 3.
For example, 29819
2 + 9 + 8 + 1 + 9 = 21
21 does not divide by 9, so 29819 is not divisible by 9

Try showing that 1233 is divisibly by 9!

Divisible by 10

This is an easy one, a number is divisible by 10 if the last digit it 0.
Examples: 540, 5230, 301290
Pretty straightforward.

Hopefully you find these techniques useful! Things are easy enough to check with a calculator, but having strong mental math is a surprisingly useful skill to have. It’s a great way to do quick sanity checks when you are solving bigger problems, and helps you avoid silly mistakes.

If you prefer video:

You can also check out more great math tutorials.