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

 It is currently 20 Sep 2019, 15:52

### 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 of 20! ?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58142
What is the rightmost non-zero digit of 20! ?  [#permalink]

### Show Tags

16 Sep 2019, 08:54
1
3
00:00

Difficulty:

55% (hard)

Question Stats:

45% (01:38) correct 55% (01:42) wrong based on 20 sessions

### HideShow timer Statistics

What is the rightmost non-zero digit of 20! ?

A. 2
B. 3
C. 4
D. 6
E. 8

_________________
Intern
Joined: 13 Aug 2019
Posts: 10
Re: What is the rightmost non-zero digit of 20! ?  [#permalink]

### Show Tags

16 Sep 2019, 11:45
1
3
To find the non zero digit the formula is

2^A A! B!

where A = 20/5 = 4 (quotient) and B is 20/5 =0 (remainder)

Now putting A and B in the formula

2^4* 4! * 0!

From the cyclicity we know that the unit digit of 2^4 would be 6

And, 4! Would have unit digit 4 (4*3*2*1=24)

Now multiplying all the unit digits:

6*4*1 =24. Therefore 4 would be the rightmost non zero digit of 20!

Posted from my mobile device
Senior Manager
Joined: 31 May 2018
Posts: 300
Location: United States
Concentration: Finance, Marketing
What is the rightmost non-zero digit of 20! ?  [#permalink]

### Show Tags

16 Sep 2019, 21:29
first of all we need to express 20! in the form of prime factors--

power of 2 in 20! = $$\frac{20}{2}$$ = $$\frac{10}{2}$$ = $$\frac{5}{2}$$ = $$\frac{2}{2}$$ = 1---10+5+2+1 = 18

power of 3 in 20! = $$\frac{20}{3}$$ = $$6/3$$ = 2 --6+2 = 8

power of 5 in 20! = $$\frac{20}{5}$$ = 4 --4

power of 7 in 20! = $$\frac{20}{7}$$ = 2 ---2

power of 11 in 20! = $$\frac{20}{11}$$ = 1 --1

power of 13 in 20! = $$\frac{20}{13}$$ = 1 ---1

power of 17 in 20! = $$\frac{20}{17}$$ = 1 --1

power of 19 in 20! = $$\frac{20}{19}$$ = 1 --1

20! (can be written as ) = 2^18*$$3^8$$*$$5^4$$*$$7^2$$*11*13*17*19 =2^14*$$3^8$$*$$7^2$$*11*13*17*19*$$10^4$$

rightmost non-zero digit of 20! = unit digit of--2^14*$$3^8$$*$$7^2$$*11*13*17*19 = 4

hence C is the correct answer
What is the rightmost non-zero digit of 20! ?   [#permalink] 16 Sep 2019, 21:29
Display posts from previous: Sort by