Divisibility Rules

For Elementary Students

What Does "Divisible" Mean?

A number is divisible by another number if you can divide it evenly with no remainder.

Think about it like this: If you can split 12 cookies evenly among 3 friends with none left over, then 12 is divisible by 3!

Example: Is 15 divisible by 5?

15 ÷ 5 = 3 (no remainder)

Yes! 15 is divisible by 5.

Example: Is 15 divisible by 4?

15 ÷ 4 = 3 R3 (remainder 3)

No. 15 is NOT divisible by 4.

Divisibility Rule for 2 (Even Numbers)

A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8 (even numbers).

Examples:

• 24 ends in 4 → divisible by 2 ✓
• 38 ends in 8 → divisible by 2 ✓
• 15 ends in 5 → NOT divisible by 2 ✗

Why it works: Even numbers can be split into 2 equal groups!

Divisibility Rule for 5

A number is divisible by 5 if it ends in 0 or 5.

Examples:

• 35 ends in 5 → divisible by 5 ✓
• 60 ends in 0 → divisible by 5 ✓
• 42 ends in 2 → NOT divisible by 5 ✗

Why it works: Think about counting by 5s: 5, 10, 15, 20... they all end in 0 or 5!

Divisibility Rule for 10

A number is divisible by 10 if it ends in 0.

Examples:

• 50 ends in 0 → divisible by 10 ✓
• 120 ends in 0 → divisible by 10 ✓
• 35 ends in 5 → NOT divisible by 10 ✗

Why it works: Every group of 10 ends in zero (10, 20, 30...).

Quick Summary

For Junior High Students

Divisibility Rule for 3

A number is divisible by 3 if the sum of its digits is divisible by 3.

Example: Is 123 divisible by 3?

Step 1: Add the digits: 1 + 2 + 3 = 6

Step 2: Is 6 divisible by 3? Yes! 6 ÷ 3 = 2

Answer: 123 is divisible by 3 ✓

Example: Is 145 divisible by 3?

Step 1: Add the digits: 1 + 4 + 5 = 10

Step 2: Is 10 divisible by 3? No. 10 ÷ 3 = 3 R1

Answer: 145 is NOT divisible by 3 ✗

Divisibility Rule for 6

A number is divisible by 6 if it's divisible by both 2 AND 3.

Example: Is 48 divisible by 6?

Check divisibility by 2: 48 ends in 8 (even) → Yes ✓

Check divisibility by 3: 4 + 8 = 12, and 12 ÷ 3 = 4 → Yes ✓

Answer: 48 is divisible by 6 ✓ (because it passes both tests)

Divisibility Rule for 9

A number is divisible by 9 if the sum of its digits is divisible by 9.

Example: Is 243 divisible by 9?

Add digits: 2 + 4 + 3 = 9

Is 9 divisible by 9? Yes! 9 ÷ 9 = 1

Answer: 243 is divisible by 9 ✓

Example: Is 456 divisible by 9?

Add digits: 4 + 5 + 6 = 15

Is 15 divisible by 9? No. 15 ÷ 9 = 1 R6

Answer: 456 is NOT divisible by 9 ✗

Divisibility Rule for 4

A number is divisible by 4 if the last two digits form a number divisible by 4.

Example: Is 1,324 divisible by 4?

Look at last two digits: 24

Is 24 divisible by 4? Yes! 24 ÷ 4 = 6

Answer: 1,324 is divisible by 4 ✓

Example: Is 1,350 divisible by 4?

Last two digits: 50

Is 50 divisible by 4? No. 50 ÷ 4 = 12 R2

Answer: 1,350 is NOT divisible by 4 ✗

Complete Divisibility Chart

Using Divisibility Rules

Why are these helpful?

Faster mental math — no need to do long division!

Checking factors — quickly find which numbers divide evenly

Simplifying fractions — know when you can reduce

Finding common denominators — helpful with fractions

Example: Simplify 45/60

Check if both are divisible by 3:

• 45: 4 + 5 = 9, divisible by 3 ✓
• 60: 6 + 0 = 6, divisible by 3 ✓

Divide both by 3: 45 ÷ 3 = 15, 60 ÷ 3 = 20

Result: 15/20 (can simplify further to 3/4)

Multiple Divisibility

Some numbers are divisible by many numbers!

Example: 60

• Ends in 0 → divisible by 2, 5, 10 ✓
• Sum of digits: 6 + 0 = 6, divisible by 3 → divisible by 3 ✓
• Last 2 digits (60) divisible by 4 → divisible by 4 ✓
• Divisible by 2 AND 3 → divisible by 6 ✓

60 is divisible by: 2, 3, 4, 5, 6, 10 (and also 1, 12, 15, 20, 30, 60)

Practice