Co-prime numbers

Co-prime is about a pair of numbers, not one number alone. 8 and 15 are co-prime. The factors of 8 are 1, 2, 4 and 8. The factors of 15 are 1, 3, 5 and 15. The only one in both lists is 1.

Neither 8 nor 15 is prime, yet the pair is co-prime. Two different prime numbers are always co-prime. Two even numbers never are, because both have 2 as a factor.

A small example

Are 45 and 63 co-prime? Break each into primes. 45 = 3 × 3 × 5 and 63 = 3 × 3 × 7. Both contain 3, so they share the factor 3 (and 9). They are not co-prime.

Now try 35 and 72. 35 = 5 × 7 and 72 = 2 × 2 × 2 × 3 × 3. No prime appears in both. So 35 and 72 are co-prime.

Why it matters later

In Class 10 Chapter 1, the HCF of two co-prime numbers is 1, and their LCM is their product. See HCF and LCM. The chapter's proof that √2 is irrational also writes it as a/b with a and b coprime, then finds a common factor. That clash is the whole proof. The Class 10 book spells the word without a hyphen.

About the author

Mohit Sardana

Chief Architect

An engineer (B.Tech, Computer Science) with over 20 years of preparing students for entrance exams, including as Dean at FIITJEE and Vice-President at Aakash. He is the chief architect of the TRUpreBoards evaluation engine.

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