Divisibility test for 6

Quick answer

A number is divisible by 6 if it passes both the divisibility tests for 2 and 3. This means the number must be even (divisible by 2) and the sum of its digits must be divisible by 3.

Learning outcome

By the end of this page, you will be able to tell if a number is divisible by 6 by checking if it is even and if the sum of its digits is divisible by 3.

• You can quickly identify if a number is divisible by 6
• You know that a number is divisible by 6 if it is even and the sum of its digits is divisible by 3
• You can apply this rule to larger numbers
• You can use this rule to solve real-world problems

Why this matters

Knowing divisibility tests helps you solve problems quickly and check your work. It's useful when sharing items equally, dividing groups, or checking if a number fits a certain pattern. For example, if you're sharing 126 sweets among 6 friends, you can quickly check if it's possible without doing long division.

In games, you might need to know if a score or number of points is divisible by 6 to unlock a special feature or win a bonus. In real life, you might be checking if a number of items can be split into equal groups of 6.

How it works

Divisibility by 6 means a number can be divided by 6 with no remainder. To check this, you need to pass two tests:

1. Is the number even? (Divisible by 2)
2. Is the sum of its digits divisible by 3?

If both tests pass, then the number is divisible by 6.

Examples you can see

Let's look at some numbers and test them for divisibility by 6:

Example 1: 18

• Is 18 even? Yes, because 18 ÷ 2 = 9 with no remainder
• Sum of digits: 1 + 8 = 9
• Is 9 divisible by 3? Yes, because 9 ÷ 3 = 3 with no remainder
• So 18 is divisible by 6

Example 2: 24

• Is 24 even? Yes, because 24 ÷ 2 = 12 with no remainder
• Sum of digits: 2 + 4 = 6
• Is 6 divisible by 3? Yes, because 6 ÷ 3 = 2 with no remainder
• So 24 is divisible by 6

Example 3: 15

• Is 15 even? No, because 15 ÷ 2 = 7 with remainder 1
• Since the first test fails, we don't need to check the second
• So 15 is NOT divisible by 6

Example 4: 72

• Is 72 even? Yes, because 72 ÷ 2 = 36 with no remainder
• Sum of digits: 7 + 2 = 9
• Is 9 divisible by 3? Yes, because 9 ÷ 3 = 3 with no remainder
• So 72 is divisible by 6

Example 5: 35

• Is 35 even? No, because 35 ÷ 2 = 17 with remainder 1
• Since the first test fails, we don't need to check the second
• So 35 is NOT divisible by 6

Try it as a mini adventure

Adventure: The Magic Number Challenge

You are a detective solving a mystery at the Math Museum. The museum's secret code is a number that is divisible by 6. You find a clue card with the number 486. You must decide if this number can unlock the treasure room. What do you do?

Step 1: Check if 486 is even

486 ends in 6, which is even. So 486 is even.

Step 2: Add the digits of 486

4 + 8 + 6 = 18

Step 3: Check if 18 is divisible by 3

18 ÷ 3 = 6 with no remainder. So 18 is divisible by 3.

Step 4: Decide

Since 486 is even and the sum of its digits (18) is divisible by 3, the number 486 is divisible by 6. You can unlock the treasure room!

Challenge: Find three more numbers that are divisible by 6 from your home. Test them using the same method.

Common mistakes

• Mistake: Thinking a number is divisible by 6 just because it's even

  Why it happens: Children might forget the second rule about the sum of digits

  Fix: Always check both tests: even AND sum of digits divisible by 3

• Mistake: Adding digits incorrectly

  Why it happens: Careless counting or forgetting a digit

  Fix: Double-check your addition and count each digit once

• Mistake: Thinking a number is divisible by 6 just because the sum of digits is divisible by 3

  Why it happens: Confusing the two tests or not checking if the number is even

  Fix: Always check if the number is even first, then check the sum of digits

• Mistake: Forgetting that 0 is divisible by 6

  Why it happens: Not understanding that 0 is even and 0 ÷ 3 = 0

  Fix: Remember that 0 is even (0 ÷ 2 = 0) and 0 is divisible by 3 (0 ÷ 3 = 0)

Parent and carer guide

Helping your child understand divisibility by 6:

1. Start with simple examples: Use small numbers like 6, 12, 18, 24 to show the pattern
2. Practice both tests: Make sure your child checks both if the number is even AND if the sum of digits is divisible by 3
3. Use visual aids: Draw arrays or groups to show how numbers can be split into 6 equal parts
4. Play games: Create a "Divisibility Detective" game where you take turns testing numbers
5. Be patient: It takes time to master these tests. Celebrate small wins
6. Connect to real life: Look for examples in daily life like sharing snacks or counting items
7. Don't rush: Let your child make mistakes and learn from them

Watch for your child to:

• Remember both tests for divisibility by 6
• Count digits carefully when adding
• Apply the rule to larger numbers
• Use the rule to solve real problems

Practice questions

1. Is 36 divisible by 6? Answer: Yes, because 36 is even and 3 + 6 = 9, which is divisible by 3
2. Is 42 divisible by 6? Answer: Yes, because 42 is even and 4 + 2 = 6, which is divisible by 3
3. Is 25 divisible by 6? Answer: No, because 25 is odd
4. Is 78 divisible by 6? Answer: Yes, because 78 is even and 7 + 8 = 15, which is divisible by 3
5. Is 123 divisible by 6? Answer: No, because 123 is odd
6. Is 90 divisible by 6? Answer: Yes, because 90 is even and 9 + 0 = 9, which is divisible by 3
7. Is 54 divisible by 6? Answer: Yes, because 54 is even and 5 + 4 = 9, which is divisible by 3
8. Is 105 divisible by 6? Answer: No, because 105 is odd
9. Is 144 divisible by 6? Answer: Yes, because 144 is even and 1 + 4 + 4 = 9, which is divisible by 3
10. Is 201 divisible by 6? Answer: No, because 201 is odd

FAQ

What does it mean for a number to be divisible by 6?

It means the number can be split into exactly 6 equal groups with nothing left over. For example, 12 apples can be shared equally among 6 friends (2 apples each).

Why do I need to check for both 2 and 3?

Because 6 = 2 × 3, so any number divisible by 6 must be divisible by both 2 and 3. If a number is divisible by 6, it must be even (divisible by 2) and its digits must add up to a multiple of 3.

Can I use this rule for really big numbers?

Yes! The rule works for any number, no matter how big. You just need to add up all the digits and check if that sum is divisible by 3.

What if a number is divisible by 6?

If a number is divisible by 6, it means you can split it into exactly 6 equal groups. You can also say that 6 is a factor of that number.

How can I remember the divisibility rule for 6?

Think of it as two-part rule: 1) Is it even? 2) Is the sum of digits divisible by 3? You can remember it as "Even AND digits add to multiple of 3".

Divisibility test for 6 facts table