Question

Numbers of ways in which 75600 can be resolved as product of two divisors which are relatively prime ?

• A. 44
• B. $8$
• C. $9$
• D. $16$

Answer 1

Answer: (B)

$8$

First we will have to find the prime factors of $75600$

Prime factorization of $75600=2\times 2\times 2\times 2\times 3\times 3\times 3\times 5\times 5\times 7$

$\Rightarrow 75600=2^4\times 3^3\times 5^2\times 7$

The number of ways in which a composite number N can be resolved as product of two divisors which are relatively prime.

$=2^{n-1}$ where n is number of different factors of N

$=2^{n-1}$

$=2^{4-1}$

$=2^3$

$=8$ ways

Hence, the answer is $8.$