Question

The power of 45 that will exactly divide 123! is:

• A. 28
• B. 30
• C. 31
• D. 59

Answer 1

The correct option is A 28

$45=3\times 3\times 5$. Here 5 is the largest prime factor of 45.
The highest power of 3 in 123! = 41 + 13 + 4 + 1 = 59
The highest power of 9 in 123! = $\frac{59-1}{2}=29$
We will find highest power of 5 in $123!=24+4=28$
The highest power of 5 in 123! is less than that of 3.
So, the highest power of 45 which divides 123! is 28.