Divisibility test for 10

Quick answer

A number is divisible by 10 if it ends in zero. You can test this by looking at the last digit of any number. If it's 0, the number is divisible by 10.

Learning outcome

By the end of this page, you will be able to tell if any number is divisible by 10 just by looking at its last digit.

• You can identify numbers that end in zero
• You can explain why a number is or isn't divisible by 10
• You can use this rule to quickly sort numbers
• You can apply this rule in games and real-life situations

Why this matters

Knowing how to quickly tell if a number is divisible by 10 helps you in many ways. When you're shopping and want to know if you can split your money evenly, when you're playing games and need to share things equally, or when you're working with money or time, this rule is super helpful. It's also a building block for understanding bigger math concepts like factors and multiples.

How it works

Let's break it down step by step:

1. Look at the last digit of any number
2. If that digit is 0, then the whole number is divisible by 10
3. If the last digit is anything other than 0, the number is NOT divisible by 10

This works because in our number system, the last digit tells us how many ones we have. When we have a number that ends in zero, it means we have no ones, just tens, hundreds, thousands, and so on. These are all perfectly divisible by 10.

Examples you can see

Let's look at some examples to see how this works:

Try this with your own numbers! Take any number and look at the last digit. If it's 0, you know it's divisible by 10.

Try it as a mini adventure

Imagine you're a treasure hunter! You've found a chest full of gold coins, and you need to divide them equally among your team of 10 friends. But first, you must figure out if you can split the coins evenly. You count them and see 350 coins.

How do you quickly know if 350 coins can be shared equally among 10 people?

Look at the last digit of 350. It's 0! That means 350 is divisible by 10. You can give each friend 35 coins and everyone gets exactly the same amount.

Now try another one: You find 247 coins. What's the last digit? It's 7. That means 247 is NOT divisible by 10, so you can't split them equally among 10 people. You'll need to find more coins or share them among fewer people.

Common mistakes

• Mistake: Thinking that numbers ending in 5 are divisible by 10
  Why it happens: Children often confuse divisibility rules for 5 and 10
  Fix: Remember that for 10, the last digit must be exactly 0
• Mistake: Looking at the first digit instead of the last digit
  Why it happens: It's easier to see the first digit, so children get confused
  Fix: Always point to the last digit and count backwards to find it
• Mistake: Forgetting that zero itself is divisible by 10
  Why it happens: Zero is a special number and can be confusing
  Fix: Remember that 0 ÷ 10 = 0, so zero is divisible by 10

Parent and carer guide

Help your child practice this rule by:

1. Playing a quick game where you say numbers and they tell you if they're divisible by 10
2. Looking around your house for numbers that end in 0 (like 10, 20, 100, 120)
3. Using real objects like coins or blocks to show how 10, 20, 30, 40 make equal groups
4. Pointing out numbers in newspapers, on clocks, or in games that end in 0
5. Encouraging them to explain why a number is or isn't divisible by 10

Remember: This is a simple rule that builds confidence. Don't worry if they make mistakes at first – it's all part of learning!

Practice questions

1. Is 45 divisible by 10? Answer: No
2. Is 70 divisible by 10? Answer: Yes
3. Is 123 divisible by 10? Answer: No
4. Is 1000 divisible by 10? Answer: Yes
5. Is 650 divisible by 10? Answer: Yes
6. Is 101 divisible by 10? Answer: No
7. Is 0 divisible by 10? Answer: Yes
8. Is 890 divisible by 10? Answer: Yes
9. Is 342 divisible by 10? Answer: No
10. Is 500 divisible by 10? Answer: Yes

FAQ

Why does the last digit matter for 10?

Because in our number system, each place value is 10 times the one to its right. The last digit is in the ones place. If it's 0, that means there are no ones, just tens, hundreds, thousands, and so on – all of which are divisible by 10.

Can negative numbers be divisible by 10?

Yes! If a negative number ends in 0, it is divisible by 10. For example, -30 is divisible by 10 because it ends in 0.

What about decimals? Can they be divisible by 10?

Decimal numbers are usually not considered in divisibility rules like this. These rules apply to whole numbers only. For example, 3.5 is not a whole number, so we don't test it for divisibility by 10.

How can I remember this rule?

Think of it like this: "If it ends in zero, it's divisible by 10." You can also imagine that 10 is like a big group of 10, so any number that ends in zero is already a complete group of 10s.

Is there a pattern with numbers divisible by 10?

Yes! All numbers divisible by 10 form a pattern: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, and so on. They all end in zero and increase by 10 each time.

Complete divisibility test for 10 facts table