Question

Determine the following numbers are co-prime.
81 and 16

Answer 1

Hint: To numbers are said to be coprime if the only common factor between them is 1. In other words, if the H.C.F. of two numbers is 1, they are said to be co-prime. To determine whether the given numbers are co-prime, we need to calculate H.C.F of both numbers. If H.C.F is 1, they are co-prime.

Complete step-by-step answer:
To determine if two numbers are co-prime, we can also list all the factors of the numbers, and if the only common factor is 1, the numbers are co-prime. For example: The factors of 81 are 1, 3, 9, 27 and 81. The factors of 16 are 1, 2, 4, 8 and 16. The only common factor among them is 1. Hence, they are co-prime. We can also use the division method to find H.C.F. Coprime should not be confused with prime numbers.
First, to find H.C.F, we express each number as a product of its prime factors.
81 can be written as:
\[81=3\times 3\times 3\times 3\]
16 can be written as:
\[16=2\times 2\times 2\times 2\]
Since, there are no common factors, H.C.F of the numbers will be 1.
As the only common factor of both the numbers is 1, the numbers are co-prime

Note: Prime numbers are individual numbers that have no factors other than 1 and itself. The term ‘co-prime’ can be used only when there are two numbers. The coprimes do not have any common factor between them.