Question

true or false. If two numbers are co.primes,at least one of them must be a prime number.​

Answer 1

False

The statement 'If two numbers are co-primes, atleast one of them must be a Prime number.' is false.

Explaining the reason:

• Two numbers are said to be prime to each other or co-primes, if their gcd or hcf is 1.

• For example, 7 and 11. These two numbers are Primes and thus their gcd is always 1. So, they are co-primes.

However it is not necessary that two numbers have to be always primes to be co-primes.

For example, 12 and 35 are co-primes, though they are not primes.

Why?

12 = 1 × 2 × 2 × 3

35 = 1 × 5 × 7

We see that, 1 is the only common factor between 12 and 35. So, their gcd is 1. Thus 12 and 35 are co-primes.

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