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

##### This topic has expert replies
Moderator
Posts: 6524
Joined: 07 Sep 2017
Followed by:20 members

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

by BTGmoderatorDC » Tue Oct 12, 2021 6:33 pm

00:00

A

B

C

D

E

## Global Stats

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

Legendary Member
Posts: 2080
Joined: 29 Oct 2017
Followed by:6 members

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

by swerve » Thu Oct 14, 2021 3:05 am
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 $$RS=(1+1)(2+1)(1+1) = 12$$

• Page 1 of 1