GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Apr 2019, 23:23

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# What is the greatest integer m for which 45^m is a factor of 48!?

Author Message
Senior Manager
Joined: 18 Feb 2019
Posts: 283
Location: India
GMAT 1: 490 Q47 V13
GPA: 3.6
What is the greatest integer m for which 45^m is a factor of 48!?  [#permalink]

### Show Tags

22 Mar 2019, 11:58
2
00:00

Difficulty:

65% (hard)

Question Stats:

55% (01:55) correct 45% (01:44) wrong based on 29 sessions

### HideShow timer Statistics

For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. What is the greatest integer m for which 45^m is a factor of 48!?

A. 1
B. 2
C. 5
D. 10
E. 11
Math Expert
Joined: 02 Aug 2009
Posts: 7570
Re: What is the greatest integer m for which 45^m is a factor of 48!?  [#permalink]

### Show Tags

22 Mar 2019, 19:47
kiran120680 wrote:
For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. What is the greatest integer m for which 45^m is a factor of 48!?

A. 1
B. 2
C. 5
D. 10
E. 11

48! is product of 1 to 48.
Now 45 =$$3^2*5$$, so here we will look at the number of 3^2 or 5, whichever is less, in the product 1*2*...47*48.
Of course, we can clearly say that there are lesser number of 3 than the number of 5, but we may have to check 3^2 vs 5
Number of 5 = $$\frac{48}{5}+\frac{48}{5^2}=9+1=10$$, we take only the integer part before the decimal, so 1.98 will be 1.
Number of 3 = $$\frac{48}{3}+\frac{48}{3^2}+\frac{48}{3^3}=16+5+1=22$$, so number of 3^2 will be 22/2=11

Now, 10 is lesser than 11, so our answer will be 10

D
_________________
Re: What is the greatest integer m for which 45^m is a factor of 48!?   [#permalink] 22 Mar 2019, 19:47
Display posts from previous: Sort by