Divisibility test for 3

Quick answer

If the sum of a number's digits is divisible by 3, then the whole number is divisible by 3. This trick helps you quickly check if a number can be shared equally among 3 people without any remainders.

Learning outcome

By the end of this page, you will be able to tell if a number is divisible by 3 just by adding up its digits – no long division needed!

• You can add the digits of any number
• You can check if that total is divisible by 3
• You can quickly say whether the whole number is divisible by 3
• You can use this trick to solve problems faster

Why this matters

Knowing if a number is divisible by 3 helps you in many everyday situations. When you're sharing things equally among 3 friends, checking if a number fits into groups of 3, or solving puzzles, this trick makes your job much easier. It's also a great way to check if your division is correct. In games and sports, you might need to split scores or points evenly, and this test helps you do that quickly.

How it works

Here’s how to check if a number is divisible by 3:

1. Add up all the digits in the number
2. Check if that total is divisible by 3
3. If yes, the original number is also divisible by 3
4. If no, the original number is not divisible by 3

Let’s try this with some examples. If you have a number like 123, you add 1 + 2 + 3 = 6. Since 6 is divisible by 3, 123 is also divisible by 3.

Examples you can see

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

Try it as a mini adventure

Adventure: The Magic Number Hunt

You are a detective on a mission to find treasure. The treasure map says the number of coins in the chest is hidden in a special code. You need to find numbers that are divisible by 3 to unlock the treasure chest. Here’s your challenge:

1. Look at the number 246
2. Add the digits: 2 + 4 + 6 = ?
3. Is this sum divisible by 3? (Hint: 3 × 2 = 6)
4. If yes, the chest will open!
5. Now try the number 579
6. Add the digits: 5 + 7 + 9 = ?
7. Is this sum divisible by 3?
8. Keep trying until you find 3 numbers that are divisible by 3

When you find a number that works, you can tell your friends or family. You’re becoming a master of the divisibility test for 3!

Common mistakes

• Mistake: Forgetting to add all the digits in a number

  Why it happens: Kids might only add the first and last digits.

  Fix: Always add all digits, even if the number is long.

• Mistake: Thinking that if the sum is 3, 6, or 9, the number is not divisible by 3

  Why it happens: Confusing the result with the rule.

  Fix: If the sum is divisible by 3 (like 3, 6, 9, 12, 15, etc.), the number is divisible by 3.

• Mistake: Not checking if the sum is actually divisible by 3

  Why it happens: Kids might not know their 3 times tables well.

  Fix: Use a 3 times table chart or count by 3s to check.

Parent and carer guide

Helping your child learn the divisibility test for 3 can be fun and easy. Here are a few tips:

• Start with small numbers like 12, 21, 33 to practice
• Use fingers or counters to add digits together
• Play a game: “Can you find a 3-digit number that’s divisible by 3?”
• Encourage your child to explain the steps to you
• Don’t worry if they make a mistake – it’s part of learning!

Remember, this is a skill that builds confidence in maths. It’s not about speed – it’s about understanding how numbers work.

Practice questions

1. Is 156 divisible by 3?
2. Is 234 divisible by 3?
3. Is 567 divisible by 3?
4. Is 891 divisible by 3?
5. Is 102 divisible by 3?
6. Is 456 divisible by 3?
7. Is 789 divisible by 3?
8. Is 333 divisible by 3?
9. Is 666 divisible by 3?
10. Is 999 divisible by 3?

Answers:

1. Yes (1 + 5 + 6 = 12, and 12 ÷ 3 = 4)
2. Yes (2 + 3 + 4 = 9, and 9 ÷ 3 = 3)
3. Yes (5 + 6 + 7 = 18, and 18 ÷ 3 = 6)
4. Yes (8 + 9 + 1 = 18, and 18 ÷ 3 = 6)
5. Yes (1 + 0 + 2 = 3, and 3 ÷ 3 = 1)
6. Yes (4 + 5 + 6 = 15, and 15 ÷ 3 = 5)
7. Yes (7 + 8 + 9 = 24, and 24 ÷ 3 = 8)
8. Yes (3 + 3 + 3 = 9, and 9 ÷ 3 = 3)
9. Yes (6 + 6 + 6 = 18, and 18 ÷ 3 = 6)
10. Yes (9 + 9 + 9 = 27, and 27 ÷ 3 = 9)

FAQ

Q: Can I use this trick for any number?

A: Yes! This trick works for any number, no matter how big it is.

Q: What if the sum of digits is a big number?

A: You can still check if it’s divisible by 3. If the sum is 15, then 15 ÷ 3 = 5, so yes, it’s divisible by 3.

Q: Why does this trick work?

A: It’s a special rule in maths. If the sum of digits is divisible by 3, then the number itself is divisible by 3. It’s like a shortcut!

Q: Is this the same as dividing by 3?

A: Not exactly. This trick only tells you if it's divisible by 3, not what the answer is. To find the actual answer, you still need to divide.

Q: Can I use this trick for other numbers too?

A: Yes! There are similar tricks for 2, 5, 9, and 10. But for 3, the digit sum is the best way to check.