Divisibility test for 4

Quick answer

If the last two digits of a number are divisible by 4, then the whole number is divisible by 4. For example, 124 is divisible by 4 because 24 is divisible by 4.

Learning outcome

By the end of this page, you will be able to tell if any number is divisible by 4 just by looking at the last two digits.

• You can quickly check if a number can be shared equally into groups of 4.
• You can use this trick to solve division problems faster.
• You can explain why this trick works with simple examples.
• You can use this test when you are working with big numbers.

Why this matters

Knowing how to quickly check if a number is divisible by 4 helps you in many ways. When you are shopping, you might want to know if you can equally share your money between 4 friends. When you are planning a party, you might need to check if the number of cupcakes or snacks can be shared equally among 4 tables. This test helps you solve problems quickly without doing long division. It's also useful when you are learning about factors and multiples, which will help you in more advanced maths later.

How it works

Let's look at how this test works step by step:

1. Look at the last two digits of any number.
2. Check if those two digits form a number that is divisible by 4.
3. If yes, the whole number is divisible by 4.
4. If no, the whole number is not divisible by 4.

For example, let's look at the number 132:

• The last two digits are 32.
• Is 32 divisible by 4? Yes, because 4 × 8 = 32.
• So, 132 is divisible by 4.

Examples you can see

Let's try some examples to see how this works:

Try this with your own numbers! Write down any number, look at the last two digits, and see if they are divisible by 4.

Try it as a mini adventure

Adventure: The Treasure Hunt

You are going on a treasure hunt. The treasure map says the number of steps to the treasure is divisible by 4. You find a note with the number 1,236. How many steps is that? You need to check if 1,236 is divisible by 4. What do you do?

1. Look at the last two digits: 36
2. Check if 36 is divisible by 4: 36 ÷ 4 = 9
3. Yes, it is divisible by 4!
4. You can take 36 steps to find the treasure!

Now, try another number: 2,457. What do you do?

1. Look at the last two digits: 57
2. Check if 57 is divisible by 4: 57 ÷ 4 = 14 remainder 1
3. No, it is not divisible by 4.
4. So, 2,457 steps is not the right number!

Can you find more numbers that are divisible by 4? Write them down and test them!

Common mistakes

• Mistake: Thinking that if the last digit is even, the number is divisible by 4.
• Why it happens: This is true for 2, but not for 4. For example, 12 is divisible by 2 but not by 4.
• Fix: Always look at the last two digits and check if they are divisible by 4.

• Mistake: Forgetting to check the whole number, not just the last digit.
• Why it happens: It's easy to get confused when working with big numbers.
• Fix: Always take the last two digits and test them.

• Mistake: Thinking that 0 is not divisible by 4.
• Why it happens: Some children think that 0 is special or doesn't work like other numbers.
• Fix: Remember that 0 ÷ 4 = 0, so 0 is divisible by 4.

Parent and carer guide

Helping your child learn this divisibility test can be fun and simple:

• Start with small numbers: Use numbers like 12, 24, 36 to show how the test works.
• Use real examples: Ask them to check if 40 or 80 can be shared equally among 4 people.
• Play games: Make up numbers and test them together. You can even make it a race!
• Be patient: It might take a few tries for them to get the hang of it.
• Encourage checking: Ask them to explain how they know a number is divisible by 4.

Remember, this is a skill that builds confidence in maths. Don't worry if they make a mistake at first – that's part of learning!

Practice questions

1. Is 148 divisible by 4? Answer: Yes, because 48 ÷ 4 = 12.
2. Is 253 divisible by 4? Answer: No, because 53 ÷ 4 = 13 remainder 1.
3. Is 304 divisible by 4? Answer: Yes, because 04 ÷ 4 = 1.
4. Is 600 divisible by 4? Answer: Yes, because 00 ÷ 4 = 0.
5. Is 717 divisible by 4? Answer: No, because 17 ÷ 4 = 4 remainder 1.
6. Is 824 divisible by 4? Answer: Yes, because 24 ÷ 4 = 6.
7. Is 932 divisible by 4? Answer: Yes, because 32 ÷ 4 = 8.
8. Is 1,001 divisible by 4? Answer: No, because 01 ÷ 4 = 0 remainder 1.
9. Is 1,236 divisible by 4? Answer: Yes, because 36 ÷ 4 = 9.
10. Is 2,457 divisible by 4? Answer: No, because 57 ÷ 4 = 14 remainder 1.

FAQ

How do I know if a number is divisible by 4?

Look at the last two digits of the number. If those two digits make a number that is divisible by 4, then the whole number is divisible by 4.

Why does this trick work?

When we divide a number by 4, we are looking at how many equal groups of 4 we can make. If the last two digits are divisible by 4, it means we can make complete groups of 4 from those digits, and the rest of the number doesn't affect this.

Can this trick be used for other numbers?

Yes! There are similar tricks for other numbers. For example, a number is divisible by 2 if the last digit is even, and by 5 if the last digit is 0 or 5. But for 4, it's always the last two digits.

What if the last two digits are 00?

If the last two digits are 00, then the number is divisible by 4 because 0 ÷ 4 = 0.

Is this trick only for big numbers?

No! You can use this trick for any number, no matter how big or small. It's especially helpful for big numbers because it saves time and effort.