Question

The co prime numbers from the following are
a.7 and 63
b.36 and 25
c.35 and 21
d.63 and 81

Answer 1

Hint: Any two numbers whose highest common factor is 1 are known as co prime numbers . so we are given four pairs of numbers and we should find the highest common factor of each pair and if it is equal to one then they are co primes

Complete step-by-step answer:
Two numbers a and b are said to be co prime if and only if their highest common factor is 1
7 and 63
Now a = 7
We know 7 is a prime number so the factors of 7 are 1 and 7
We have b = 63
The factors of 63 are 1 , 3 , 7 , 9 , 21 , 63.
Therefore the common factors of a and b are 1 and 7
From this the highest common factor is 7
Since the highest common factor is$7 \ne 1$ .
 7 and 63 are not co-prime numbers
36 and 25
Now a = 25
We know the factors of 25 are 1 , 5 and 25
We have b = 36
The factors of 36 are 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 36.
Therefore the common factors of a and b is 1
From this the highest common factor is 1
 Since the highest common factor is $1 = 1$ .
25 and 36 are co-prime numbers.
From this we can conclude that the correct option is b.

Note: 1. Prime numbers are always coprime to each other.
2. Any two consecutive integers are always coprime.
3. Sum of any two coprime numbers is always coprime to their product.
4. 1 is trivially coprime with all numbers.