Question

If $P=2^4\cdot 6^3\cdot 5^2\cdot {15}^2$, then the number of proper odd divisors of $P$ will be

• A. $29$
• B. $30$
• C. $59$
• D. $60$

Answer 1

The correct option is A $29$

$P=2^4\cdot 6^3\cdot 5^2\cdot {15}^2$
$\Rightarrow P=2^4\cdot (2\times 3{)}^3\cdot 5^2\cdot (3\times 5{)}^2$
$\Rightarrow P=2^7\cdot 3^5\cdot 5^4$
Therefore, the number of odd proper divisors
$=(5+1)(4+1)-1=29$