How many factors of the number 2^9*3^6*5^5*10^4 are multiples of

Question

How many factors of the number  2^9*3^6*5^5*10^4  are multiples of 60?

A. 594
B. 648
C. 980
D. 1200
E. 2100

Are You Up For the Challenge: 700 Level Questions

Danush649 · Answer

60= 2^2*3*5
Give number n= 2^2*3*5( 2^11* 3^5 * 5^8)
Number of factors= (11+1) * (5+1) * ( 8+1)
= 648

Posted from my mobile device

nivivacious · Answer

We can rewrite : 2^9*3^6*5^5*10^4 as
 2^13*3^6*5^9
Divide this by 60 ie 2^2*5*3 
You get 2^11* 3^5 * 5^8
Therefore add 1 to each exponent
(11+1)(5+1)(8+1)
= 648
Ans: B

Abhishek009 · Answer

60 = 2^2*3*5

2^9*3^6*5^5*10^4=2^{13}*3^6*5^9

On dividing we have - \frac{2^{13}*3^6*5^9}{2^2*3*5}=2^{11}*3^5*5^8

No of factors of the above will be  (11+1)(5+1)(8+1)=648 , Answer must be (B)

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

How many factors of the number 2^93^65^5*10^4 are multiples of

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions