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