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# 14! is equal to which of the following?

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Math Expert
Joined: 02 Sep 2009
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14! is equal to which of the following? [#permalink]

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20 Apr 2016, 00:04
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14! is equal to which of the following?

A. 87,178,291,200
B. 88,180,293,207
C. 89,181,294,209
D. 90,000,000,003
E. 91,114,114,114
[Reveal] Spoiler: OA

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Re: 14! is equal to which of the following? [#permalink]

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20 Apr 2016, 00:48
For sure it ends even number
that's A / E

since we have 10 in the multiplication, its A (ending with 0)
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Re: 14! is equal to which of the following? [#permalink]

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20 Apr 2016, 01:02
2
KUDOS
Every factorial higher than 4! will have 0 as a units digit, so answer must be A
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Math Expert
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Posts: 5649
Re: 14! is equal to which of the following? [#permalink]

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20 Apr 2016, 01:56
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Bunuel wrote:
14! is equal to which of the following?

A. 87,178,291,200
B. 88,180,293,207
C. 89,181,294,209
D. 90,000,000,003
E. 91,114,114,114

since 14! is PRODUCT of all numbers till 14, it should end in 0s in units and tens place.. as lower integer value of [] in $$[\frac{14}{5}] + [\frac{14}{5^2}]= 2$$
ONLY A has two 0s in end..
A
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Re: 14! is equal to which of the following? [#permalink]

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20 Apr 2016, 06:44
chetan2u wrote:
Bunuel wrote:
14! is equal to which of the following?

A. 87,178,291,200
B. 88,180,293,207
C. 89,181,294,209
D. 90,000,000,003
E. 91,114,114,114

since 14! is PRODUCT of all numbers till 14, it should end in 0s in units and tens place.. as lower integer value of [] in $$[\frac{14}{5}] + [\frac{14}{5^2}]= 2$$
ONLY A has two 0s in end..
A

Can you explain the solution more ? why do you divide 14/5 ?
Math Expert
Joined: 02 Aug 2009
Posts: 5649
14! is equal to which of the following? [#permalink]

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20 Apr 2016, 06:52
ghofran wrote:
chetan2u wrote:
Bunuel wrote:
14! is equal to which of the following?

A. 87,178,291,200
B. 88,180,293,207
C. 89,181,294,209
D. 90,000,000,003
E. 91,114,114,114

since 14! is PRODUCT of all numbers till 14, it should end in 0s in units and tens place.. as lower integer value of [] in $$[\frac{14}{5}] + [\frac{14}{5^2}]= 2$$
ONLY A has two 0s in end..
A

Can you explain the solution more ? why do you divide 14/5 ?

hi,
this is the method to find number of 5 in 14!..
since 14! contains 1*2*3..*5*..*9*10*11..14, 14/5=2.8 -- lower integer is 2--you can see it has two 5 in its product- 5 and 10..
so what you are doing by dividing is you are finding the multiple of 5 till 14..
the moment it is 15!.. our answer is 15/5 =3 so 5,10 and 15...

say it goes up to 25!..
here we have 25/5 + 25/5^2+ 25/5^3.. = 5+1+0=6..
the 6 are ONE each in 5,10,15,20 and TWO in 25..

very important concept in FACTORIALS..
Please let me know if there is some query
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14! is equal to which of the following? [#permalink]

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20 Apr 2016, 06:59
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Bunuel wrote:
14! is equal to which of the following?

A. 87,178,291,200
B. 88,180,293,207
C. 89,181,294,209
D. 90,000,000,003
E. 91,114,114,114

This problem can be solved at a glance, no need of calculation.

14! is divisible by 5 and hence the units digit will be 0

Among the given options only (A) follows.
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Re: 14! is equal to which of the following? [#permalink]

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20 Apr 2016, 07:46
after 4!, every factorial last digit ends in 0.
5!=120
6!=720.

so only option A last digit ends with 0.
So option A is correct.
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Re: 14! is equal to which of the following? [#permalink]

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20 Apr 2016, 08:54
Abhishek009 wrote:
Bunuel wrote:
14! is equal to which of the following?

A. 87,178,291,200
B. 88,180,293,207
C. 89,181,294,209
D. 90,000,000,003
E. 91,114,114,114

This problem can be solved at a glance, no need of calculation.

14! is divisible by 5 and hence the units digit will be 0

Among the given options only (A) follows.

Disagree
The way to solve by only a glance is that it is divisible by 5 and 2 both(you wrote it is divisible by 5)
E.G 25 is divisible by 5 and it ends in 5 too

Small technical error .
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14! is equal to which of the following? [#permalink]

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20 Apr 2016, 09:18
stonecold wrote:
Abhishek009 wrote:
Bunuel wrote:
14! is equal to which of the following?

A. 87,178,291,200
B. 88,180,293,207
C. 89,181,294,209
D. 90,000,000,003
E. 91,114,114,114

This problem can be solved at a glance, no need of calculation.

14! is divisible by 5 and hence the units digit will be 0

Among the given options only (A) follows.

Disagree
The way to solve by only a glance is that it is divisible by 5 and 2 both(you wrote it is divisible by 5)
E.G 25 is divisible by 5 and it ends in 5 too

Small technical error .

I agree U are dividing by 2 but consider this -

5! = 5*4*3*2*1 =>5^1*3^1*2^3

Check there are 3 two's that doesn't mean there will be 3 zeros in 5!

Remember this short little form { Something I learnt during my CAT days }

Quote:
The number of trailing zeroe's in a factorial is the highest power of 5

I am just working around the same form to answer the question quickly....

Check this formula to any factorial - 10,15 ,20....... ( U will get it )

Further for this problem a quick glance at the options U will notice only option (A) has a trailing 0, so U need to find if the factorial is divisible by 5 or not.....

Now with your example -

Quote:
E.G 25 is divisible by 5 and it ends in 5 too

No of 5s in 25! is -

25/5 = 5
5/5 =1

Total no of 5's in 25! is 6 ( 5+ 1)

No of 2s in 25! is -

25/2 = 12
12/2 = 6
6/2 = 3
3/2 = 1

Total no of 2's in 25! is 22 ( 12+6+3+1)

In 25 ! (No of 5's < No of 2's)

So, 25 ! will have 6 zero's in the end, though no of 2's in 25! is more than no of 5's.

Hope I am clear...
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Thanks and Regards

Abhishek....

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Location: United States (LA)
Re: 14! is equal to which of the following? [#permalink]

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12 Sep 2017, 11:31
After 4! any factorial number must end in unit's digit as 0
we don't need to actually calculate the value of 14!
So the answer is straightforward option A
Re: 14! is equal to which of the following?   [#permalink] 12 Sep 2017, 11:31
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# 14! is equal to which of the following?

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