Question

If a natural number, $N =2^3 \cdot 3^2 \cdot 5^1 \cdot 7^1$ then identify which of the following statement(s) is(are) correct?

• A. The product of all divisors of $N$ is $( N )^{24}$
• B. The product of all even divisors of $N$ is $(2 N )^{18}$
• C. The product of all odd divisors of $N$ is $\left(\frac{ N }{2}\right)^6$
• D. The product of all composite divisors of $N$ is $\left(\frac{ N ^{24}}{210}\right)$

Answer 1

Answer: (A), (B), (D)

Correct answer is (a) The product of all divisors of $N$ is $( N )^{24}$Correct answer is (b) The product of all even divisors of $N$ is $(2 N )^{18}$Correct answer is (d) The product of all composite divisors of $N$ is $\left(\frac{ N ^{24}}{210}\right)$