Co-prime numbers
Cut a 14 m ribbon and a 15 m ribbon. Make equal pieces of one size. Each piece must be a whole number of metres. Only 1 m pieces work.
Loading lab…
Step 1 of 4
- Factors of 15 and 14, side by side.
- Only the number 1 is on both lists.
- Add the factors of 21. It shares 1 and 7 with 14.
- 14 and 21 share more than 1.
Sharing only 1
Two numbers are co-prime when 1 is the only factor they share. Their HCF is 1.
| Pair | Factors they share | Co-prime? |
|---|---|---|
| 14, 15 | 1 | Yes |
| 14, 21 | 1, 7 | No |
| 9, 25 | 1 | Yes |
| 18, 24 | 1, 2, 3, 6 | No |
Three patterns help you find co-prime pairs quickly.
- Two numbers that differ by 1 are co-prime. For example, 14 and 15. A number going into both also goes into the gap between them. The gap is 1, and only 1 goes into 1.
- Two different primes are co-prime. Each has only 1 and itself as factors.
- Two even numbers are not co-prime. Both have the factor 2.
Watch out!
Co-prime does not mean prime. 9 = 3 × 3 and 25 = 5 × 5, so neither is prime. Yet they share only 1.