Question

Let $N=2^3\times 3^5\times 5^7,$ then which of the following statement is false about N ?

• A. Number of proper divisors of N is equal to 192
• B. Sum of all divisors of N divisible by 3 but not by 12 equals to 80
• C. Number of divisors of N equals to $(2^4-1)\left(\frac{3^6-1}{2}\right)\left(\frac{5^8-1}{4}\right)$
• D. If a and b are coprime numbers then number of pairs (a,b) such that $a\times b=N$ are equal to 8

Answer 1

Answer: (A)

Number of proper divisors of N is equal to 192

$N=2^3\times 3^5\times 5^7$

No. of proper divisions $=4\times 6\times 8=192$

We know no. of divisions $=(3+1)\times (5+1)\times (7+1)$

Hence clearly option C is incorrect.