Question

If two numbers are relatively prime or co-prime, then their HCF is _____________.
A) \[5\]
B) \[0\]
C) \[1\]
D) \[9\]

Answer 1

Hint- We need learn few definitions such as:
Prime number: A number is called a prime number if it has only two factors 1 and itself. For example, 13, 17 and so on.
Co-prime number: If a set of integers has only one common factor and that is 1, the numbers are called co-prime numbers. For examples,
The factors of 13 are 1 and 13.
The factors of 17 are 1 and 17.
So, the common factors of 13 and 17 is 1. Hence, these two are co-prime numbers.
Co-prime numbers are also called the relatively prime numbers.
HCF: The full form of HCF is the highest common factor.

Complete step by step answer:
Let us consider, \[a,b\] to be two relatively or co-prime numbers. To find its HCF, at first, we will find their factors.
Factors of \[a\]is \[1,a\]
Factors of \[b\]is \[1,b\]
So, the common factor of \[a,b\]is \[1\]. It is the highest common factor also.
Hence, two numbers are relatively prime or co-prime, then their HCF is \[1\].

Note – For coprime or relatively prime numbers it is not necessary that the two numbers have to be prime. Any one number could be composite. For example,
Factor of 12 are 1, 2, 3, 4, 6, 12
Factors of 17 are 1,17.
The common factor of 12 and 17 is 1.
So, they are co-prime or relatively prime numbers.
The HCF is also known as GCD, which is the greatest common divisor.