Divisibility and Divisibility Rules
A number is divisible by another when it divides exactly, with no remainder. Divisibility rules are quick digit checks for this: a number is divisible by 2 when its last digit is even.
Video Lesson
Watch and learn the basics
🎬 Did this video explain it clearly?
Flashcards
Review key concepts visually
%20Divisibility.webp)
%20Divisibility%20Rules%20for%202%2C4%2C8.webp)
%20Divisibility%20Rules%20for%203%2C6%2C9.webp)
%20Divisibility%20Rules%20for%205%2C%2010.webp)
What Does Divisible Mean?
- A number is divisible if it divides exactly with no remainder.
- For example, (divisible), but (not divisible).
Divisibility Rules for 2, 4, and 8
- A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
- A number is divisible by 4 if the last two digits are divisible by 4.
- A number is divisible by 8 if the last three digits are divisible by 8.
Divisibility Rules for 3, 6, and 9
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- A number is divisible by 6 if it is divisible by both 2 and 3.
- A number is divisible by 9 if the sum of its digits is divisible by 9.
Divisibility Rules for 5 and 10
- A number is divisible by 5 if the last digit is 0 or 5.
- A number is divisible by 10 if the last digit is 0.
Practice Questions
Test your understanding
Is 124 divisible by 2?
Correct! 🎉 +10 pointsNot quite right
124 is an even number, which means it is divisible by 2. Any number that ends in 0, 2, 4, 6, or 8 is divisible by 2.
Which of the following numbers is divisible by 5?
Correct! 🎉 +10 pointsNot quite right
A number is divisible by 5 if it ends in 0 or 5. Among the options, only 40 ends in 0, making it divisible by 5.
Is 542 divisible by 3?
Correct! 🎉 +20 pointsNot quite right
To check if 542 is divisible by 3, add its digits: . Since 11 is not divisible by 3, 542 is not divisible by 3.
Is 675 divisible by 9?
Correct! 🎉 +20 pointsNot quite right
To check if 675 is divisible by 9, add its digits: . Since 18 is divisible by 9, 675 is also divisible by 9.
Which of the following numbers is divisible by 8?
Correct! 🎉 +20 pointsNot quite right
To check if a number is divisible by 8, the last three digits must be divisible by 8. Only 432 meets this condition.
Is 528 divisible by 6?
Correct! 🎉 +30 pointsNot quite right
For a number to be divisible by 6, it must be divisible by both 2 and 3. Since 528 is even (divisible by 2) and is divisible by 3, 528 is divisible by 6.
Want to see the full working?
Interactive Activity
Click to test divisibility rules and see which digits matter.
Loading interactive widget...
Students Also Ask
The questions students bump into most on this topic
A number is divisible by 3 when the sum of its digits is divisible by 3. For example, the digits of 543 add up to 5 + 4 + 3 = 12. Since 12 is divisible by 3, the number 543 is also divisible by 3.
A number is divisible by 4 when its last two digits form a number that is divisible by 4. For example, 328 ends in 28, and 28 is divisible by 4. So the whole number 328 is divisible by 4.
A number is divisible by 8 when its last three digits form a number that is itself divisible by 8. For example, 6160 ends in 160. Since 160 is divisible by 8, the whole number 6160 is divisible by 8 as well.
A number is divisible by 9 when the sum of its digits is divisible by 9. For example, the digits of 198 add up to 1 + 9 + 8 = 18. Because 18 is divisible by 9, the number 198 is divisible by 9.
Check the last digit. A number is divisible by 2 when its last digit is even, meaning 0, 2, 4, 6 or 8. It is divisible by 5 when the last digit is 0 or 5. It is divisible by 10 when the last digit is 0.
A remainder is the amount left over when one number does not divide exactly into another. For example, sharing 9 bananas between 2 friends gives each friend 4, with 1 left over. That leftover is the remainder, and it is always smaller than the divisor.