Arithmetic Foundation Quiz #2 Q1

[Zarina]

Dear all,

Would you be so kind to help with the following problem
this question is from Arithmetic foundation quiz #2, which was taken from this article - The Importance of a Strong Quant Foundation - GregMat

It is clear that to the right it is 2^200. To the left side have toubles to transform to something comparable to the right side. Tried to find how many 2s, 5s are there in 100!, taking into account that 100! has tons of factors it seems daunting. Wondering if there is alternative way to solve this question.

Thank you

[Leaderboard]

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[Zarina]

thank you, amended the post

[Leaderboard]

Think about this a bit differently. On the RHS, you’re multiplying a small number many times. On the LHS, you are multiplying increasingly larger numbers. Which do you think would be greater?

[Zarina]

Many thanks!