Question

$N=2^3\times 3^2\times 5^3\times 10.$ If P is a natural number, then how many factors of N are of the form $2P+1$?

• A. 14
• B. 15
• C. 13
• D. 12

Answer 1

The correct option is A 14

$N=2^4\times 3^2\times 5^4$. Ultimately, we need to find out the number of odd factors of N except 1. Number of odd factors (including 1) $=(2+1)\times (4+1)=3\times 5=15.$

Answer- $(15-1)=14$.