Divisibility Test

Divisibility test

Here are some quick tricks (called divisibility test) you can learn to see if a number is divisible (can be divided by) another number. How!

OK … … You can see that 27 is divisible by 3 which means 3 goes to 27.

But, can you quickly tell if 3 goes into 537? Without doing long division? I can! And not just because I’m super math brilliant — because I know some math tricks. These are ways to learn because they will save you a lot of time!

Divisibility by 2 Test

A number is divisible by 2 if it is even.

Here’s another way to define this one:

A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8.

Let’s do try an easy example?

Does 2 go into 20?

(Is 20 divisible by 2?)

Yep, since the last digit is 6.

(It’s even!)

Here harder example:

Is 290986 divisible by 2?

Yes, since the last digit is 6.

(It’s even)

What about this one?

Is 2719 divisible by 2?

No, since the last digit is 9 and it’s not an even number.

Try yourself: Is 869539 divisible by 2?

Divisibility by 5 Test

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

Let’s do try an easy example?

Is 25 divisible by 5?

Yep, since the last digit is 5.

(Check your result by a calculator or do some long division)

Here harder example:

Is 495380 divisible by 5?

Yes, since the last digit is 0.

What about this one?

Is 9826827 divisible by 5?

No, since the last digit is not a 0 or 5.

Divisibility by 10 Test

There is the easiest one!

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

Is 50 divisible by 10?  Yes!

Is 899 divisible by 10? No!

YOUR TURN:

Is 389 divisible by 2?

Is 789 divisible by 10?

Is 8963 divisible by 5?

Is 589635 divisible by 2?

Is 2568634 divisible by 5?

Is 3890 divisible by 10?

The next two tricks are some harder, but once you get good at them, you can do them easily!

Divisibility by 3 Test

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

WHY?!

Don’t worry —- this is easy!

Let’s do one:

Does 3 go into 2610?

  • Add the digits

12 + 6 + 1 +0 = 9

  • Does 9 is divisible by 3?

Yep!

So, 2610 is divisible by 3!

(Check your result by a calculator or do some long division)

Here’s another one:

Does 3 go into 80354?

8 + 0 + 3 + 5 + 4 = 20

3 does not go into 20,

So, 80354 is not divisible by 3!

Divisibility by 9 Test

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

Let’s do one:

Is 7821 divisible by 9?

 

  • Add the digits

7 + 8 + 2 + 1 = 18

  • Is 18 divisible by 9?

Yep!

So, 7821 is divisible by 9!

(Check your result by a calculator or do some long division)

Here’s another one:

Does 9 go into 80354?

8 + 0 + 3 + 5 + 4 = 20

9 does not go into 20,

Check out the answer for the “nines” time tables!

9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108

TRY IT:

Is 270 divisible by 3?

Is 270 divisible by 9?

Is 863544 divisible by 3?

Is 5555289 divisible by 9?

Is 2583250 divisible by 3?

Divisibility by 6 Test

A number is divisible by 6 if it is divisible by 2 AND 3.

So, you just do the test for 2 and the test for 3 … If they both satisfy, then you are right way to go!

Check out example:

Is 36 divisible by 6?

  • 36 is even (last digit is 2), so

36 is divisible by 2….

  • 3 +6 = 9 which is divisible by 3…

So, 36 is divisible by 6!

What about this one?

Does 6 go into 54863?

No, it is not even so 2 doesn’t go in.

TRY IT:

Does 6 go into 9864?

Does 6 go into 6666?

Does 6 go into 8262?

Divisibility by 4 Test

This one works great – about half of the time.

A number is divisible by 4 if the last two digits are a number that’s are divisible 4.

Let me make that clear:

Look at the following number

78948

Is 48 divisible by 4? Yep!

So, the number is divisible by 4.

Try it another:

Is 123 divisible by 4? Nope!

Last two digit 23 is not divisible by 4.

Divisibility by 8 Test

This is a lot similar the test for 4, but even less useful.

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

a number that’s divisible by 8.

Therefore, we have to look at a three digits number, we’re probably not going to

Be able to eyeball this one. We’ll probably need to do some long division.

Is 900200 divisible by 8?

Ok, we just need to check to see if 8 goes into 200.

Long division Time!

8) 200 (25

    – 16

40

  -40

00

So, 985200 is divisible by 8.

How about this one?

Is 98066 divisible by 8?

Hey, this one is very easy! Is 66 is divisible by 8?

No way. So, 98066 doesn’t divisible by 8.

YOUR TASK:

Is 869655 is divisible by 4?

Is 366558255 is divisible by 8?

Is 2258692222655 is divisible by 4?

Is 236799655 is divisible by 8?

Is 109281655 is divisible by 4?

Is 1129655 is divisible by 8?