Free Practice Question

PS · Problem Solving

sub-505

Divisibility/Multiples/Factors

Determine the largest positive integer $y$ for which $3^y$ divides $9!$ .

Answer Choices

Correct answer marked below

A

1

B

2

C

3

4

Correct

E

5

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Explanation

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Official Explanation

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We need to find the largest positive integer y such that 3^y divides 9!. To do this, we will calculate the highest power of 3 that divides 9!. We can…

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A

AmaanDec 17, 2024

Thanks for sharingThank you for sharing!!thanks for sharing

E

EndeApr 25, 2024

Thank you very much!

What this question tests

What it tests

Your understanding of divisibility rules, least common multiples, and greatest common factors.

Common trap

Forgetting that 1 is not prime and that every integer divides 0.

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Determine the largest positive integer yyy for which 3y3^y3y divides 9!9!9!.