Question

Find the highest power of 5625 that can exactly divide 565!.

• A. 34
• B. 35
• C. 32
• D. 30

Answer 1

The correct option is A

34

$5625=5^4\times 3^2$.
$\therefore$ Highest power of 5625 in 565! will depend on the highest power of $5^4$.
So, highest power of $5^4$ in 565! is = Integral value of $\frac{113+22+4}{4}$ = 34.