GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 25 May 2020, 00:17

### 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 rightmost non-zero digit in 15!?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 64070
What is the rightmost non-zero digit in 15!?  [#permalink]

### Show Tags

25 Feb 2020, 01:04
00:00

Difficulty:

75% (hard)

Question Stats:

43% (01:57) correct 57% (01:54) wrong based on 61 sessions

### HideShow timer Statistics

What is the rightmost non-zero digit in 15!?

A. 2
B. 4
C. 6
D. 8
E. 9

Project PS Butler

Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS

Are You Up For the Challenge: 700 Level Questions

_________________
Director
Joined: 25 Jul 2018
Posts: 712
What is the rightmost non-zero digit in 15!?  [#permalink]

### Show Tags

25 Feb 2020, 01:52
3
1
What is the rightmost non-zero digit in 15!?

—>[ $$\frac{15}{5}$$ ] ...= 3 (there are three zeroes at the end of 15!; $$5^3$$)

—> $$[\frac{15}{2}]+ [\frac{15}{4}]+ [\frac{15}{8}]+...= 7+3+1= 11$$ (—> $$2^{11}$$ )

—> $$[\frac{15}{3}]+ [\frac{15}{9}]+...= 5+1 = 6$$( —> $$3^6$$)

—> $$[\frac{15}{7}]+...= 2$$ (—> $$7^{2}$$)

So, $$15! = 2^{11}* 3^{6} *5^{3} *7^{2}*11*13$$

And eliminate the zeroes:
—> $$\frac{15!}{1000}= 2^8*3^6*7^2*11*13$$

Now, just find the units digits and multiply one another to get the last digit —> ...6*...9...*9...*1...*3 = ...18...* 81 = ...8

The rightmost nonzero digit of 15! is 8

The answer is D.

Posted from my mobile device
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4990
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Re: What is the rightmost non-zero digit in 15!?  [#permalink]

### Show Tags

25 Feb 2020, 06:44
1
Bunuel wrote:
What is the rightmost non-zero digit in 15!?

A. 2
B. 4
C. 6
D. 8
E. 9

Project PS Butler

Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS

Are You Up For the Challenge: 700 Level Questions

15/5 = 3 => A

Remainder is 0 =>B

So, Last Non zero digit will be $$2^A*A!*B!$$

= $$2^3*3!*0!$$

= 8* 6* 1

=>8 , Hence Answer must be (D) 8
_________________
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 )
GMATWhiz Representative
Joined: 07 May 2019
Posts: 693
Location: India
Re: What is the rightmost non-zero digit in 15!?  [#permalink]

### Show Tags

25 Feb 2020, 12:00
1
Bunuel wrote:
What is the rightmost non-zero digit in 15!?

A. 2
B. 4
C. 6
D. 8
E. 9

Solution

• We know that 5! = 1*2*3*4*5 = 120
• So rightmost non-zero digit in 5! = 2
• If we multiply the rightmost non-zero digit of 5! to 6, the unit digit of the resulting number will give the rightmost non-zero digit of 6!
o i.e. rightmost non-zero digit in 6! = unit’s digit of $$(2*6) = 2$$
• Following the same pattern as above we get,
o Rightmost non-zero digit in 7! = unit' s of ((rightmost non-zero digit in 6! )*7)= unit’s digit of $$(2*7) =4$$
o Rightmost non-zero digit in 8! = unit’s digit of $$(4*8) = 2$$
o Rightmost non-zero digit in 9! = unit’s digit of $$(2*9) =$$unit’s digit of $$18 = 8$$
o Rightmost non-zero digit in 10! = ten’s digit of $$(2*9*10)$$ =ten’s digit of $$(18*10) = 8$$
 We have taken ten’s digit because we know that on multiplying a number by 10, the unit’s digit will always be 0 and we want right-most non-zero digit.
o Rightmost non-zero digit in 11! = unit’s digit of $$(8*1) = 8$$
o Rightmost non-zero digit in 12! = unit’s digit of $$(8*2) = 6$$
o Rightmost non-zero digit in 13! = unit’s digit of $$(6*3) = 8$$
o Rightmost non-zero digit in 14! = unit’s digit of $$(8*4) =$$ unit’s digit of $$32= 2$$
o Rightmost non-zero digit in 15! = ten’s digit of $$(32*15)$$= ten’s digit of $$(32*15) = 8$$
Thus, the correct answer is Option D.
_________________

GMAT Prep truly Personalized using Technology

Prepare from an application driven course that serves real-time improvement modules along with a well-defined adaptive study plan. Start a free trial to experience it yourself and get access to 25 videos and 300 GMAT styled questions.

Score Improvement Strategy: How to score Q50+ on GMAT | 5 steps to Improve your Verbal score
Study Plan Articles: 3 mistakes to avoid while preparing | How to create a study plan? | The Right Order of Learning | Importance of Error Log
Helpful Quant Strategies: Filling Spaces Method | Avoid Double Counting in P&C | The Art of Not Assuming anything in DS | Number Line Method
Key Verbal Techniques: Plan-Goal Framework in CR | Quantifiers the tiny Game-changers | Countable vs Uncountable Nouns | Tackling Confusing Words in Main Point
GMATWhiz Representative
Joined: 07 May 2019
Posts: 693
Location: India
Re: What is the rightmost non-zero digit in 15!?  [#permalink]

### Show Tags

25 Feb 2020, 23:09
Bunuel wrote:
What is the rightmost non-zero digit in 15!?

A. 2
B. 4
C. 6
D. 8
E. 9

Solution

• $$15! = 1*2*3*4*5*6*7*8*9*10*11*12*13*14*15$$
o $$15! =1*2*3*(2^2)*5*(2*3)*7*(2^3)*(3^2)*(2*5)*11*(2^2*3)*13*(2*7)*(3*5) = 2^{11}*3^6*5^3*7^2*11*13$$
• $$2^3*5^3$$ will give three 0, and we want rightmost nonzero, so ignoring it we get
• Rightmost non – zero digit of 15! = unit’s digit of $$(2^8*3^6*7^2*11*13) ………. (i)$$
o Unit’s digit of $$(7^2*11*13) =$$ Unit’s digit of $$(9*1*3) = 7 ……. (ii)$$
o Cyclicity of powers of 3 is 4, so units digit of $$3^6 = 9 ………. (iii)$$
o Also, Cyclicity of powers of 2 is 4, so units digit of $$2^8 = 6 …. (iv)$$
• Thus, from (i), (ii), (iii) and (iv) we can write,
o Rightmost non – zero digit of $$15! =$$ unit’s digit of $$(7*9*6) = 8$$
Thus, the correct answer is Option D.
_________________

GMAT Prep truly Personalized using Technology

Prepare from an application driven course that serves real-time improvement modules along with a well-defined adaptive study plan. Start a free trial to experience it yourself and get access to 25 videos and 300 GMAT styled questions.

Score Improvement Strategy: How to score Q50+ on GMAT | 5 steps to Improve your Verbal score
Study Plan Articles: 3 mistakes to avoid while preparing | How to create a study plan? | The Right Order of Learning | Importance of Error Log
Helpful Quant Strategies: Filling Spaces Method | Avoid Double Counting in P&C | The Art of Not Assuming anything in DS | Number Line Method
Key Verbal Techniques: Plan-Goal Framework in CR | Quantifiers the tiny Game-changers | Countable vs Uncountable Nouns | Tackling Confusing Words in Main Point
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 3975
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
What is the rightmost non-zero digit in 15!?  [#permalink]

### Show Tags

26 Feb 2020, 03:06
Bunuel wrote:
What is the rightmost non-zero digit in 15!?

A. 2
B. 4
C. 6
D. 8
E. 9

Project PS Butler

Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS

Are You Up For the Challenge: 700 Level Questions

$$15!= 1*2*3*4*5*6*7*8*9*10*11*12*13*14*15$$

$$15!= 2^{11}*3^6*5^3*7^2*11*13 = (2*5)^3*2^8*3^6*7^2*11*13 = 10^3*6*9*9*1*3 = 10^3*8$$

i.e. 8 will be the rightmost non-zero digit

_________________
Prosper!!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
Online One-on-One Skype based classes l Classroom Coaching l On-demand Quant course
Check website for most affordable Quant on-Demand course 2000+ Qns (with Video explanations)
Click for FREE Demo on VERBAL & QUANT
Our SUCCESS STORIES: Getting Reborn!!! From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
ACCESS FREE GMAT TESTS HERE:22 FREE (FULL LENGTH) GMAT CATs LINK COLLECTION
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 10540
Location: United States (CA)
Re: What is the rightmost non-zero digit in 15!?  [#permalink]

### Show Tags

28 Feb 2020, 07:41
1
Bunuel wrote:
What is the rightmost non-zero digit in 15!?

A. 2
B. 4
C. 6
D. 8
E. 9

Project PS Butler

Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS

Are You Up For the Challenge: 700 Level Questions

15! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 x 15

= 2 x 3 x 2 x 2 x 5 x 6 x 7 x 8 x 9 x 2 x 5 x 11 x 12 x 13 x 14 x 3 x 5

= (2 x 2 x 2 x 5 x 5 x 5) x 3 x 6 x 7 x 8 x 9 x 2 x 11 x 12 x 13 x 14 x 3

As we can see from the above, 15! has 3 factors of 5; therefore, we pair them with 3 factors of 2 so that the 3 factors of 2 and 3 factors 5 (i.e., the factors in the parentheses) become 1000. This tells us that 15! has 3 trailing zeros, and the rightmost non-zero digit (i.e., the first non-zero digit to the left of the 3 trailing zeros) will be determined by the units digit of the product of the factors outside of the parentheses. So let’s determine that units digit by recording the units digits as we multiply them, starting from 3 x 6 and proceeding to the right:

3 x 6 → 8

8 x 7 → 6

6 x 8 → 8

8 x 9 → 2

2 x 2 → 4

4 x 11 → 4

4 x 12 → 8

8 x 13 → 4

4 x 14 → 6

6 x 3 → 8

We see that the rightmost non-zero digit is 8.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
202 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

CEO
Joined: 03 Jun 2019
Posts: 2889
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Re: What is the rightmost non-zero digit in 15!?  [#permalink]

### Show Tags

28 Mar 2020, 03:40
Bunuel wrote:
What is the rightmost non-zero digit in 15!?

A. 2
B. 4
C. 6
D. 8
E. 9

Project PS Butler

Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS

Are You Up For the Challenge: 700 Level Questions

Asked: What is the rightmost non-zero digit in 15!?

15! = 15*14*13*12*11*10*9*8*7*6*5*4*3*2 = 6*14*13*12*11*9*8*7*6*3*1000

Rightmost non-zero digit = Unit digit of 6*4*3*2*9*8*7*6*3 = Unit digit of 2*2*2 = 8

IMO D
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
CEO
Joined: 03 Jun 2019
Posts: 2889
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Re: What is the rightmost non-zero digit in 15!?  [#permalink]

### Show Tags

28 Mar 2020, 03:42
Abhishek009 wrote:
Bunuel wrote:
What is the rightmost non-zero digit in 15!?

A. 2
B. 4
C. 6
D. 8
E. 9

Project PS Butler

Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS

Are You Up For the Challenge: 700 Level Questions

15/5 = 3 => A

Remainder is 0 =>B

So, Last Non zero digit will be $$2^A*A!*B!$$

= $$2^3*3!*0!$$

= 8* 6* 1

=>8 , Hence Answer must be (D) 8

Hi Abhishek009
Please explain highlighted part.
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Re: What is the rightmost non-zero digit in 15!?   [#permalink] 28 Mar 2020, 03:42

# What is the rightmost non-zero digit in 15!?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne