Question

show that 143 and 187 are not coprime

Answer 1

Concept we will be using:
i) Two  numbers are said to be co-prime, if their HCF is 1.
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Solution:

The given two numbers are 143 and 187.

To check whether the two numbers are co-prime or not, we have to find the HCF.

Step 1: Prime factorize both the numbers.
143 = 13 x 11
187 = 17 x 11

Step 2: Identify the HCF (highest common factor).
Observe that,  the two numbers have only 11 as the common factor.
HCF = 11

Therefore, 143 and 187 are not co-prime because their HCF is 11 and not 1.
 
Answer : 143 and 187 are not co-prime because their HCF is 11.

Answer 2

Solution :-

Prime factorization of 143 = 11*13
Prime factorization of 187 = 11*17
11 is the common factor of 143 and 187.
So the H.C.F. of 143 and 187 is 11

So, 143 and 187 are not co-prime because the co-prime numbers have 1 as their only factor.
So, hence it is proved that 143 and 187 are not co-prime because 11 is also their factor other than 1.

Answer.