If r is divisible by 10 and s is divisible by 9, rs must have at least how many factors?

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If r is divisible by 10 and s is divisible by 9, rs must have at least how many factors?

(A) Two
(B) Four
(C) Twelve
(D) Fourteen
(E) Sixteen


OA C

Source: Manhattan Prep

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BTGmoderatorDC wrote:
Tue Oct 12, 2021 6:33 pm
If r is divisible by 10 and s is divisible by 9, rs must have at least how many factors?

(A) Two
(B) Four
(C) Twelve
(D) Fourteen
(E) Sixteen


OA C

Source: Manhattan Prep
Minimum value of \(R=10\) and minimum value of \(S=9\)

So, the minimum value of \(RS=90\)

Now, prime factorizing \(90\) gives \(2^1 3^2 5^1\)

Therefore, the number of factors of \(RS=(1+1)(2+1)(1+1) = 12\)