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What is the right most non-zero digit in the value of 15!

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What is the right most non-zero digit in the value of 15!  [#permalink]

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New post 23 Aug 2019, 23:34
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What is the right most non-zero digit in the value of 15!
A. 1
B. 2
C. 4
D. 6
E. 8

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What is the right most non-zero digit in the value of 15!  [#permalink]

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New post Updated on: 24 Aug 2019, 03:27
1
EncounterGMAT wrote:
What is the right most non-zero digit in the value of 15!
A. 1
B. 2
C. 4
D. 6
E. 8


Asked: What is the right most non-zero digit in the value of 15!

15! = 15*14*13*12*11*10*9*8*7*6*5*4*3*2*1
15! has 3 0s.
To find out right most non-zero digit in 15! we can find unit digit of 15!/1000

To remove 0s from 15!
5*2*10 = 10*10= 100
15 * 4= 60
2*4*5*10*15 = 6000 = 6*1000
We can remove 2,4,5,10,15 and replace them with 6

Unit digit of 15! /1000= Unit digit of (6*4*3*2*1*9*8*7*6*3) = 8 after removing tens digits from 14,13,12,11
The right most non-zero digit in 15! is 8

IMO E
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Originally posted by Kinshook on 23 Aug 2019, 23:51.
Last edited by Kinshook on 24 Aug 2019, 03:27, edited 1 time in total.
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Re: What is the right most non-zero digit in the value of 15!  [#permalink]

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New post 24 Aug 2019, 02:43
Kinshook wrote:
EncounterGMAT wrote:
What is the right most non-zero digit in the value of 15!
A. 1
B. 2
C. 4
D. 6
E. 8


Asked: What is the right most non-zero digit in the value of 15!

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

To remove 0s from 15!
5*2*10 = 10*10= 100
15 * 4= 60
We can remove 2,4,5,10
,15 and replace them with 6


Unit digit of 15! = Unit digit of (6*4*3*2*1*9*8*7*6*3) = 8 after removing tens digits from 14,13,12,11

IMO E


Kinshook
please explain the highlighted part of your solution why digit 6 has been placed?
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Re: What is the right most non-zero digit in the value of 15!  [#permalink]

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New post 24 Aug 2019, 02:52
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1
This way might not be the shortest way but it can be used to solve to find for any value of n in n!

first write all the primes below N. and then find the powers of those primes in n!

for example, here the primes less than N are 2,3,5,7,11,13

The powers of 2 are 11,
powers of 3 are 6,
powers of 5 are 3
powers of 7 are 2
power of 11 is 1
and powers of 13 is 1.

now since 2^3 * 5^3 gives the powers of 10. so remove those.

we need to check the rightmost non zero digit, so essentially we need the unit digit.

now 2 and 3 have a cyclicity of 4.
so the remaining 2^8 = 2^4 which gives a unit digit of 6.
and 3^6 = 3^(4+2) so it becomes 3^2 which gives a unit digit of 9.
now 7^2 has a unit digit of 9.

the product reduces to
6*9*9*1*3,
after performing this calculation we get the answer as 8.

Option E satisfies that.


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Re: What is the right most non-zero digit in the value of 15!  [#permalink]

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New post 24 Aug 2019, 02:52
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Archit3110 wrote:
Kinshook wrote:
EncounterGMAT wrote:
What is the right most non-zero digit in the value of 15!
A. 1
B. 2
C. 4
D. 6
E. 8


Asked: What is the right most non-zero digit in the value of 15!

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

To remove 0s from 15!
5*2*10 = 10*10= 100
15 * 4= 60
We can remove 2,4,5,10
,15 and replace them with 6


Unit digit of 15! = Unit digit of (6*4*3*2*1*9*8*7*6*3) = 8 after removing tens digits from 14,13,12,11

IMO E


Kinshook
please explain the highlighted part of your solution why digit 6 has been placed?


Archit3110

To find out right most non-zero digit we have to remove 0s and then find out unit digit of remaining number.
To remove 0s
We have to eliminate 5,10 & 15 with power of 2s.
Let us choose 5*2, 10 & 15*4 randomly
2*4*5*10*15 = 6000 = 6*1000
Then remove these numbers from 15! and replace them with 6 and then find out unit digit of 15!/1000.
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What is the right most non-zero digit in the value of 15!  [#permalink]

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New post Updated on: 29 Aug 2019, 17:34
Kinshook

I deleted my explanation. I think it is wrong. Sorry about that.

Originally posted by chondro48 on 29 Aug 2019, 16:34.
Last edited by chondro48 on 29 Aug 2019, 17:34, edited 3 times in total.
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Re: What is the right most non-zero digit in the value of 15!  [#permalink]

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New post 29 Aug 2019, 17:11
chondro48 wrote:
EncounterGMAT and Kinshook, kindly evaluate my solution.

Q. What is the right most non-zero digit in the value of 15!?
A. 1
B. 2
C. 4
D. 6
E. 8

After reading the question, I immediately know what the question really asks: what is the units digit of multiplication of factors of 2 in 15! (2x4x6x...x14)

15! has 7 multiples of 2 (2, 4,...,14) and therefore, factors of 2^11. So the units digit of multiplication of 2^11 is 8.

Answer is (E)


@chondo48

If I use this logic, right most non zero digit in 6! = 720 Should have been 2*4*6 = 48 or 8 which is incorrect

But if you remove 2*5 = 10 from 6! Then 1*3*4*6 = 72 will provide correct answer

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Re: What is the right most non-zero digit in the value of 15!   [#permalink] 29 Aug 2019, 17:11
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