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

 It is currently 19 Oct 2019, 07:51

### 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 maximum value of m such that 7^m divides into 14! evenly?

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 02 Jan 2017
Posts: 293
What is the maximum value of m such that 7^m divides into 14! evenly?  [#permalink]

### Show Tags

Updated on: 15 Jul 2019, 03:45
1
1
3
00:00

Difficulty:

5% (low)

Question Stats:

82% (00:47) correct 18% (01:02) wrong based on 65 sessions

### HideShow timer Statistics

What is the maximum value of m such that 7^m divides into 14! evenly?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

Source: Nova GMAT
Difficulty Level: 500

Originally posted by vikasp99 on 05 Mar 2017, 09:25.
Last edited by SajjadAhmad on 15 Jul 2019, 03:45, edited 1 time in total.
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4773
Location: India
GPA: 3.5
Re: What is the maximum value of m such that 7^m divides into 14! evenly?  [#permalink]

### Show Tags

05 Mar 2017, 10:07
1
vikasp99 wrote:
What is the maximum value of m such that 7^m divides into 14! evenly?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

Highest power of 7 that will evenly divide 14! will be -

$$\frac{14}{7} = 2$$

Hence, answer will be (B) 2
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Intern
Joined: 11 Aug 2016
Posts: 46
Location: India
Concentration: Operations, General Management
Schools: HBS '18, ISB '17, IIMA
GMAT 1: 710 Q49 V38
GPA: 3.95
WE: Design (Manufacturing)
Re: What is the maximum value of m such that 7^m divides into 14! evenly?  [#permalink]

### Show Tags

05 Mar 2017, 11:40
3
To calculate the highest power of a prime number in the factorial of a number, we need to do a continued division until the quotient is 0.

Example
What is the highest power of 5 that divides 25!?

First we divide 25 by 5 => the quotient is 5 and the remainder is 0.
Next, we divide the quotient in the previous step by 5. The new quotient is 1 and the remainder is 0.
Next we divide the quotient again by 5. The new quotient is 0 and the remainder is 1.

Now adding all the quotients, we 5+1+0=6.

So the highest power of 5 that divides 25! is 6.

Similarly applying the same method to 14!, we get

Divide 14 by 7 => quotient is 2 and remainder 0
Divide 2 by 7 => quotient is 0 and remainder is 2.

Adding all quotients we get 2+0=2

Highest value of m = 2

Manhattan Prep Instructor
Joined: 04 Dec 2015
Posts: 832
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Re: What is the maximum value of m such that 7^m divides into 14! evenly?  [#permalink]

### Show Tags

05 Mar 2017, 13:46
1
vikasp99 wrote:
What is the maximum value of m such that 7^m divides into 14! evenly?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

Translate this problem as 'How many 7s are there in 14!'. The translation is the hard part! But, think of it as a fraction with 7^m in the denominator. That is, the fraction looks like this:

14*13*12*11*...*2*1 / (7*7*7*7*...7) (m times).

You want to know how many of those 7s you can have, and have them still cancel out (resulting in an integer).

You can only cancel out two 7s: one by turning the 14 in the numerator into a 2, and one by crossing out the 7 in the numerator.
_________________

Chelsey Cooley | Manhattan Prep | Seattle and Online

My latest GMAT blog posts | Suggestions for blog articles are always welcome!
Intern
Joined: 20 Dec 2018
Posts: 46
Re: What is the maximum value of m such that 7^m divides into 14! evenly?  [#permalink]

### Show Tags

22 Dec 2018, 03:42
14! = 14 x 13 x 12 x 11 x ……………. x 1.
So, maximum power of 7 that would evenly divide 14! Would be 2 because in 14! There are just 2 no divisible by 7 i.e. 14 and 7.
Hence, maximum value of m = 2.
Re: What is the maximum value of m such that 7^m divides into 14! evenly?   [#permalink] 22 Dec 2018, 03:42
Display posts from previous: Sort by