Factors, multiples, primes, GCF & LCM
← Back to Math TopicsNumber theory studies whole numbers and how they fit together. Let's meet the key ideas.
Factors of 12: 1, 2, 3, 4, 6, 12
Numbers that divide evenly with no remainder.
Multiples of 4: 4, 8, 12, 16, 20…
What you get from the times table of a number.
2, 3, 5, 7, 11, 13, 17, 19…
Exactly two factors: 1 and itself.
4, 6, 8, 9, 10, 12…
More than two factors. (1 is neither prime nor composite.)
Every whole number can be broken down into a product of prime numbers. This is like finding a number's DNA!
GCF(12, 18) = 6
The biggest number that divides both. Great for simplifying fractions.
LCM(4, 6) = 12
The smallest number that both divide into. Great for adding fractions.
Quick tricks to check if one number divides another without doing the division:
| Divisible by | Rule | Example |
|---|---|---|
| 2 | Ends in 0, 2, 4, 6, or 8 | 34 ✓ |
| 3 | Digit sum is divisible by 3 | 72 → 7+2=9 ✓ |
| 4 | Last two digits divisible by 4 | 128 → 28 ✓ |
| 5 | Ends in 0 or 5 | 85 ✓ |
| 6 | Divisible by both 2 and 3 | 54 ✓ |
| 9 | Digit sum is divisible by 9 | 81 → 8+1=9 ✓ |
| 10 | Ends in 0 | 250 ✓ |