Divisibility Rules

Is this number divisible by 2, 3, or 5?

Photo by Photos Hobby on Unsplash

It’s helpful to be able to tell just by looking at a number if it can be divided by 2, 3 or 5, with no remainder (in other words, no decimal). This will come in handy in the future when determining if a number is a prime or a composite. There are a few tips that can help!

Divisible by 2:

If a number ends in an even number (0, 2, 4, 6, 8), it’s divisible by 2.

3,928 ends in an 8, which is an even number, so 3,928 is divisible by 2.

3,927 ends in 7 which is an odd number, so 3,927 is not divisible by 2.

Divisible by 3:

If you add up the numbers that make up the number, and that sum is divisible by 3, the number is divisible by 3.

117 would be added up as 1 + 1 + 7 = 9, and 9 is divisible by 3, so 117 is divisible by 3. (I know, how did you go your whole life without this fun trick?!)

218 would be added up as 2 + 1 + 8 = 11, and 11 is not divisible by 3, so 218 is not divisible by 3.

Divisible by 5:

If a number ends in 0 or 5, it’s divisible by 5.

Example: 4,394,985 ends in a 5, so it’s divisible by 5.

4,394,984 does not end in a 0 or a 5, so it is not divisible by 5.

4,394,980 ends in a 0, so it is divisible by 5.

There are more rules (divisibility by 4, 5, 6, 7, 8, 9, 10, 11, 12), but the above are building blocks. If you can spot the divisibility by 2, 3, or 5, you can break a number down using those tools. 

What about the number in the photo at the top of the post: 2006.

Is it divisible by 2? Yes, since it ends in an even number (6), it is.

Is it divisible by 3? No, since 2 + 0 + 0 + 6 = 8, and 8 is not divisible by 3, it is not.

Is it divisible by 5? No, since it ends in a 6, not a 0 or a 5, it is not.

Try some on your own (scroll to the end of the post for answers):

Want more practice? You can make up your own problems, here’s how:

Write down a number here:

Is it divisible by 2?

Is it divisible by 3?

Is it divisible by 5?

Now check your own work. Let’s say you wrote 5,210.

Is it divisible by 2? Yes, you think it is.

Check it with a calculator: 5210/2 = 2605. There is no decimal, so it is divisible by 2. You got it right!

Is it divisible by 3? No, you don’t think it is.

Check it with a calculator: 5210/3 = 1736.6667. There is a decimal, so the 3 did not go into 5210 cleanly. It is not divisible by 3. You got another one right.

Is it divisible by 5? Yes, you think it is.

Check it with a calculator: 5210/5 = 1042. There is no decimal, so it is divisible by 5. You got it right!

Answers to the table above: