Question

How many factors of $2^5\times 3^6\times 5^2$ are perfect squares?

• A. $24$
• B. $12$
• C. $16$
• D. $22$

Answer 1

Answer: (A)

$24$

For perfect square , the power of each should be even

Factor of $2^5$

Possiblities : $\left(2^0\right),\left(2^2\right),\left(2^4\right)⟶$ Ways

Factor of $3^6$

Possiblities : $\left(3^0\right),\left(3^2\right),\left(3^4\right),\left(3^6\right)⟶4$ Ways

Factor of $5^2$

Possiblities : $\left(5^0\right),\left(5^2\right)⟶2$ Ways

Total number of ways

$=4\times 3\times 2=24$ Ways