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

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1
3 00:00

Difficulty:   55% (hard)

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

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

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

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

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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!

C is the right answer.

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

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

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