Question

The least possible number with which (180)! should be multiplied so that it can be divided by $(45{)}^{44}$ is:

• A. 44
• B. 25
• C. 9
• D. none of these

Answer 1

The correct option is D none of these

$(45{)}^{44}=(3^2\times 5{)}^{44}=3^{88}\times 5^{44}$
Let's check for the power of 5 in 180!
180! = $5^{43}\times$ some number.
As the highest power of 5 in 180! is 43 & in order to be divisible by $(3^{88}\times 5^{44})$, it needs to have at least one more 5.
Hence, the least possible number to be multiplied with 180! is 5.