Question

Determine the following numbers are co-prime.
$15$ and $37$.

Answer 1

Hint: Co- prime numbers are the numbers which have only one common factor between them and that common factor is 1. So, the HCF of the co-prime numbers must always be equal to 1. So, to check whether 15 and 37 are co-prime numbers or not, we need to find their factors and see whether the only common factor between them is 1 or not.

Complete step by step solution:
In this question, we are given two numbers and we need to check if these numbers are co – prime are not.
The given numbers are: 15 and 37
Now, first of all, let us see what co prime numbers are.
In mathematics, co-prime numbers are the numbers which have only one common factor between them and that common factor is 1. So, the HCF of the co-prime numbers must always be equal to 1. Co-prime numbers are also known as relatively prime or mutually prime numbers. So, to check whether 15 and 37 are co primes or not, we need to find their factors.
Let us find the factors of 15 first.
$ \Rightarrow $Factors of 15$ = 1 \times 3 \times 5$
Now, let us see the factors of 37
$ \Rightarrow $Factors of 37$ = 1 \times 37$
Here, we can see that the only common factor between 15 and 37 is 1. And also the HCF of 15 and 37 is 1.

So, therefore, we can say that 15 and 37 are co-prime numbers.

Note:
> 1 is co-prime with all the integers.
> Any two prime numbers are always co-prime to each other.
> Any two successive numbers are always co-prime. For example: 2 and 3, 5 and 6, 9 and 10 are co-primes.
> Two even numbers can never be co-primes.