How can you easily tell if a large number is divisible by 24?
The number 24 is made up of the factors 3 and 8. This is important, because you can quickly test if a number is divisible by 3 and 8 — and if both tests pass, then the number is divisible by 24.
Step 1: Divisibility by 8
To check if a number is divisible by 8, look at the last three digits of the number.
This works because multiples of 8 repeat every 1,000, so if the last three digits form a number divisible by 8, then the entire number is divisible by 8.
Step 2: Divisibility by 3
To check if a number is divisible by 3, add all its digits together. If the result is divisible by 3, then so is the number.
If both tests pass, the original number is divisible by 24.
Example: Is 62,472 divisible by 24?
Step 1: Take the last three digits: 472
$472 \div 8 = 59$ — a whole number ✅Step 2: Add the digits:
$6 + 2 + 4 + 7 + 2 = 21$
$21 \div 3 = 7$ — a whole number ✅
Since 62,472 is divisible by both 8 and 3, it is divisible by 24.
Indeed: $62,472 \div 24 = 2,603$
Try it yourself — pick a large number and see if both rules apply.
A Fun Fact: Product of Four Consecutive Numbers
The product of any four consecutive integers is always divisible by 24.
Why? Among any four consecutive numbers, you will always find:
- A multiple of 2
- A multiple of 3
- A multiple of 4
Since $2 \times 3 \times 4 = 24$, the total product is divisible by 24.
Try it:
Let’s take $5, 6, 7, 8$
$$ 5 \times 6 \times 7 \times 8 = 1680 \ 1680 \div 24 = 70 $$
A clean result.
Summary
To check if a number is divisible by 24:
- Check if the last three digits are divisible by 8
- Check if the sum of all digits is divisible by 3
If both are true, then the number is divisible by 24.