Question

H.C.F of two co prime is:
a)1
b)2
c)0
d)3

Answer 1

Hint: Find logically what the common factors of co-primes and then proceed.

Complete step-by-step answer:

In the question we have H.C.F of two co prime numbers.

At first, we briefly understand H.C.F or the highest common factor.

In mathematics, the highest common factor or H.C.F of two or more integers, which are not at all zeros, the largest positive integer that divides each of the integers. For example, the h.c.f of 8 and 12 is 4.

In the name highest common factor, the adjective highest can be replaced by greatest; and the word fact or that can be replaced by divisor, so that the names include greatest common divisor (gcd).

Let’s know one of the properties of co-prime numbers which are as follows:

       1 is coprime to every number.

Every prime number is co-prime to each other. As every prime number has only two factors 1 and number itself, the common factor of two prime numbers will be 1. For example: 2, 3. Factors of 2 are 1 and 2 and that of 3 is 1 and 3. So, the common factor is 1, hence, co-prime.
Any two successive numbers or integers are always coprime. For example: 2,3 or 3,4 and so on.

So, the HCF of two coprime numbers is 1.

Hence, the correct option is ‘A’.


Note: There is also a special property of coprime numbers is that the sum of any two coprime numbers is always coprime to the product of co-primes. For example: 2,3 ; their sum is 5 and product is 6.