What Does "Divisible" Mean?
A number is divisible by another number if dividing gives a remainder of zero — in other words, it divides evenly. Divisibility rules let you check this quickly just by looking at the digits.
The Rules
Divisible by 2
A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
Example: 4 836 → last digit 6 (even) → divisible by 2 ✓
Divisible by 3
A number is divisible by 3 if the sum of its digits is divisible by 3.
Example: 4 836 → 4 + 8 + 3 + 6 = 21, and 21 ÷ 3 = 7 → divisible by 3 ✓
Divisible by 4
A number is divisible by 4 if its last two digits form a number divisible by 4.
Example: 4 836 → last two digits: 36, and 36 ÷ 4 = 9 → divisible by 4 ✓
Divisible by 5
A number is divisible by 5 if its last digit is 0 or 5.
Example: 3 250 → last digit 0 → divisible by 5 ✓
Example: 4 836 → last digit 6 → not divisible by 5 ✗
Divisible by 9
A number is divisible by 9 if the sum of its digits is divisible by 9.
Example: 4 836 → 4 + 8 + 3 + 6 = 21, and 21 ÷ 9 = 2 R 3 → not divisible by 9 ✗
Example: 3 456 → 3 + 4 + 5 + 6 = 18, and 18 ÷ 9 = 2 → divisible by 9 ✓
Divisible by 10
A number is divisible by 10 if its last digit is 0.
Example: 5 400 → last digit 0 → divisible by 10 ✓
Divisibility Summary
For 9: digit sum divisible by 9. For 10: last digit is 0. For 4: last two digits divisible by 4.
Checking Multiple Rules at Once
Which of 2, 3, 5, 9, 10 divide 2 340?
- Last digit: 0 → divisible by 2 ✓, divisible by 5 ✓, divisible by 10 ✓
- Digit sum: 2 + 3 + 4 + 0 = 9 → divisible by 3 ✓, divisible by 9 ✓
2 340 is divisible by all of 2, 3, 5, 9, and 10.
A Quick Note on Prime Numbers
A prime number is a whole number greater than 1 that is only divisible by 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23 …
The divisibility rules above help you check that a number is not prime (because it is divisible by something other than 1 and itself).
Real-World Applications
Real world: dividing items into equal groups
A teacher has 72 stickers to hand out equally. Can she divide them into groups of 3? Into groups of 9?
Digit sum of 72: 7 + 2 = 9. 9 ÷ 3 = 3 ✓ and 9 ÷ 9 = 1 ✓
Yes to both. 72 ÷ 3 = 24 stickers per group of 3; 72 ÷ 9 = 8 stickers per group of 9.
Real world: arranging chairs in rows
An auditorium has 480 chairs. The organiser wants equal rows. Which row sizes from work?
Last digit: 0 → by 2 ✓, by 5 ✓, by 10 ✓. Digit sum: 4+8+0 = 12 → by 3 ✓. Last two digits: 80, 80÷4=20 → by 4 ✓. Digit sum 12, 12÷9 = 1 R 3 → by 9 ✗.
Rows of 2, 3, 4, 5, or 10 all work; rows of 9 do not.
Common Mistakes
- Applying the digit-sum rule to check divisibility by 2 (it only works for 3 and 9)
- Forgetting that the rule for 4 uses the last two digits, not just the last one
- Thinking that all even numbers are divisible by 4 (e.g. 14 is even but 14 ÷ 4 = 3 R 2)
Practice Problems
Is 3 852 divisible by 2, 3, 4, 9?
Show answer
A baker has 250 rolls. Can she pack them into bags of 5? Into bags of 9?