Question

Example for co-prime numbers is
A) $27,14$
B) $18,16$
C) $9,18$
D) $11,77$

Answer 1

Hint: Here we will check which one of the given options are co-prime numbers. Firstly we will write the definition of co-prime numbers then by using the factors of the numbers we will check whether they are co-prime or not. Finally we will get our desired answer.

Complete step-by-step answer:
$27,14$
We will write the factors of each number as,
$27 = 3 \times 3 \times 3 \times 1$
$14 = 2 \times 7 \times 1$
As we can see there is no common factor between the two numbers except 1.
So $27,14$ are co-prime numbers.
$18,16$
We will write the factors of each number as,
$18 = 2 \times 3 \times 3 \times 1$
$16 = 2 \times 2 \times 2 \times 2 \times 1$
As we can see there are two common factors between the two numbers which are$1,2$.
So $18,16$ are not coprime numbers.
$9,18$
We will write the factors of each number as,
$9 = 3 \times 3 \times 1$
$18 = 2 \times 3 \times 3 \times 1$
As we can see there are two common factors between the two numbers which are$1,3$.
So $9,18$ are not coprime numbers.
$11,77$
We will write the factors of each number as,
$11 = 11 \times 1$
$77 = 7 \times 11 \times 1$

As we can see there are two common factors between the two numbers which are$1,11$.
So $11,77$ are not coprime numbers.
Hence, option (A) is correct.

Note:
Co-prime numbers are those numbers whose common factor is 1 and there are no other common factors between them. We can also say that H.C.F of those numbers is 1 they are also known as ‘Relatively Prime Numbers’. Every prime number is co-prime to each other. All successive numbers are always coprime. If we add or multiply two co-prime numbers we always get a co-prime number.