14! is equal to which of the following?

Question

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

paidlukkha · Answer

For sure it ends even number
that's A / E

since we have 10 in the multiplication,  its A  (ending with 0)

mathiaskeul · Answer

Every factorial higher than 4! will have 0 as a units digit, so answer must be A

chetan2u · Answer

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    +  = 2 
ONLY A has two 0s in end..
A

ghofran · Answer

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

chetan2u · Answer

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

Abhishek009 · Answer

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. :-D

Psiva00734 · Answer

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.

stonecold · Answer

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 .

Abhishek009 · Answer

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 } 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 ) :-D

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 - 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. :lol:

Hope I am clear...

rhine29388 · Answer

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

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14! is equal to which of the following?

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14! is equal to which of the following?

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