Divisibility test for 8

Quick answer

If you want to know if a large number is divisible by 8, you only need to check if the last three digits of that number form a number that is divisible by 8.

Learning outcome

By the end of this page, you will be able to test if any large number is divisible by 8 by looking only at the last three digits.

Success signs:

• You can quickly tell if a number is divisible by 8
• You can check the last three digits and decide if they are divisible by 8
• You can explain why checking the last three digits works
• You can use this trick to solve bigger division problems

Why this matters

Knowing how to quickly check if a number is divisible by 8 is helpful in many situations. You might be sorting a big pile of items into groups of 8, checking if a number fits a pattern, or solving puzzles where you need to divide by 8. It’s also useful when you’re doing division with big numbers and want to double-check your work. This trick makes it easier to do mental maths and saves time when you're checking division.

How it works

Here’s how to test if a number is divisible by 8:

1. Look at the last three digits of the number
2. Check if that three-digit number is divisible by 8
3. If yes, then the whole number is divisible by 8
4. If no, then the whole number is not divisible by 8

This works because 1000 is divisible by 8, so the thousands and higher place values don’t change the remainder when dividing by 8. Only the last three digits matter for the remainder.

Examples you can see

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

Example 1: Is 1,232 divisible by 8?

• Look at the last three digits: 232
• Is 232 divisible by 8? Let’s check: 232 ÷ 8 = 29
• Yes, 232 is divisible by 8
• So, 1,232 is also divisible by 8

Example 2: Is 4,567 divisible by 8?

• Look at the last three digits: 567
• Is 567 divisible by 8? Let’s check: 567 ÷ 8 = 70.875
• No, 567 is not divisible by 8
• So, 4,567 is not divisible by 8

Example 3: Is 10,000 divisible by 8?

• Look at the last three digits: 000 (or just 0)
• Is 0 divisible by 8? Yes, 0 ÷ 8 = 0
• So, 10,000 is divisible by 8

Try it as a mini adventure

Imagine you are a detective trying to solve a mystery. A secret code has been left, and it says “The number of treasure chests is divisible by 8.” The number you found is 7,648. You need to figure out if this number is divisible by 8 to unlock the treasure.

Let’s solve it together:

1. Look at the last three digits of 7,648: 648
2. Check if 648 is divisible by 8: 648 ÷ 8 = 81
3. Yes! 648 is divisible by 8
4. So, 7,648 is also divisible by 8
5. You can now open the treasure chest!

Common mistakes

• Mistake: Thinking that if the last digit is even, the number is divisible by 8.
• Why it happens: Confusing divisibility rules for 2 and 8. The rule for 2 only checks the last digit.
• Fix: Remember, only the last three digits matter for 8. You must divide the last three digits by 8 to check.

• Mistake: Checking only the last two digits instead of the last three.
• Why it happens: Mistaking the rule for 4 (which only looks at the last two digits) for 8.
• Fix: Always look at the last three digits when testing for 8.

• Mistake: Forgetting that 0 is divisible by 8.
• Why it happens: Thinking that 0 is too small or doesn’t count.
• Fix: Remember, any number times 0 is 0, so 0 is divisible by any number (including 8).

Parent and carer guide

As a parent or carer, you can help your child by:

• Practising with numbers of different sizes together
• Using real-world examples like counting items in groups of 8
• Reinforcing that only the last three digits matter
• Checking that your child understands why this trick works
• Encouraging them to try the trick with numbers they find in daily life, like house numbers or prices

What to say:

• “Let’s try this trick with a big number you saw today!”
• “What do you notice about the last three digits?”
• “If the last three digits are divisible by 8, what does that tell us about the whole number?”

What not to worry about:

• Your child might make a mistake at first – that’s normal
• They might get confused with the rule for 4 or 2 – this is common
• Don’t rush them; take time to explain and practice

Practice questions

1. Is 3,456 divisible by 8?
2. Is 1,288 divisible by 8?
3. Is 9,000 divisible by 8?
4. Is 7,532 divisible by 8?
5. Is 12,344 divisible by 8?

Answers:

1. Yes – 456 ÷ 8 = 57
2. Yes – 288 ÷ 8 = 36
3. Yes – 000 ÷ 8 = 0
4. No – 532 ÷ 8 = 66.5
5. Yes – 344 ÷ 8 = 43

FAQ

Why does checking the last three digits work for 8?

Because 1000 is divisible by 8 (1000 ÷ 8 = 125), the thousands and higher place values don’t change the remainder when dividing by 8. Only the last three digits (hundreds, tens, and units) affect whether the whole number is divisible by 8.

Can I use this trick for any number?

Yes! This trick works for any number, no matter how big. You just need to look at the last three digits and see if they are divisible by 8.

What if the last three digits are 000?

If the last three digits are 000, that means the number is divisible by 8. Zero divided by 8 is 0, so it works!

Is there a trick for 4 too?

Yes! For 4, you only need to check the last two digits. This is different from 8, where you check the last three digits.

How can I remember this rule?

Think of it like this: “For 8, look at the last three digits.” You can make a rhyme like, “To test for 8, check the last three – if they divide by 8, so does the whole thing!”