Question

Number of ways in which a composite number $N$ can be resolved into two factors, which are prime to each other if $N$ is of the form $2^2 3^2 5^2 7^2$, is

• A. $2$
• B. $2^2$
• C. $2^4$
• D. $2^3$

Answer 1

Answer: (D)

Here co-prime numbers are $2, 3, 5, 7$
Counted prime numbers $= 4$
(Fact) The number of ways in which a composite number $N$ can be broken into two factors, which are prime to each other is $2^{n - 1}$.
$\therefore $ Required number of ways $= 2^{n- 1}$
$= 2^{4 - 1} = 2^3 = 8$