The integer 50! ends in how many zeros?

Question

A. 5
B. 8
C. 10
D. 11
E. 12

Showmeyaa · Answer

All that the question is asking is how many pairs of (5*2) can be formed from 50!
Please see that the number of 5's will be less than the number of 2's. So, if we can get the number of 5's in 50!, we should be good.
 \frac{50!}{5} = 10 
 \frac{50!}{25 }= 2 
10 + 2 = 12
So, IMO (E)!

ankitgoswami · Answer

10s : 10, 20, 30, 40, 50 
5 x 2 = 10 : 5,15,25,35,45
Additional 5s : one additional 5 in 25 and one in 50

So total = 5 + 5 + 2
 = 12

IMO  E

Aliprep · Answer

Calculated in excel and found that the actual number is 30 414 093 201 713 400 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000.00
Which actually has much more zeroes than answers. 
Are these kind of problems will be on real GMAT?

GMATWhizTeam · Answer

Solution:

As far as the question on trailing zero is concerned, there is a direct formal to it.

The number of trailing zero in n! can be calculated through:  \frac{n}{5} + \frac{n}{5^2} + \frac{n}{5^3} + .... \frac{n}{n^k}  where  5^{k+1} > n

So calculating by formula, the number of trailing zero in  50! = \frac{50}{5} + \frac{50}{25} = 10 + 2 = 12

However, if you want to understand this logic behind then here is the second method:

Alternate Solution:

We know  50! = 50 	imes 49 	imes 48 	imes 47 	imes ....... 	imes 1

Every  0  will come from  2	imes 5 . So we basically need to calculate how many  2	imes 5  do we have in  50! .

We can see that there are more  2's  than  5's  therefore if we calculate the number of  5's  we can get the answer.

So the number of multiples of  5  between  1  to  50   = \frac{50}{5} = 10

So the number of multiples of  25  between  1  to  50   = \frac{25}{5} = 2

Thus the right answer  = 10+2 = 12

Hence the right answer is  Option E .

Bunuel · Answer

Excel is not good when calculating large numbers. 15! actually equals to 30414093201713378043612608166064768844377641568960512000000000000. Check here: https://www.wolframalpha.com/input/?i=3 ... Math%22%7D Theory on Trailing Zeros: https://gmatclub.com/forum/everything-ab ... 85592.html For more check Trailing Zeros Questions and Power of a number in a factorial questions in our Special Questions Directory . Hope this helps.

zhengdeji · Answer

Number Factorial
1 1
2 2
3 6
4 24
5 120
6 720
7 5040
8 40320
9 362880
10 3628800
11 39916800
12 479001600
13 6227020800
14 87178291200
15 1.30767E+12
16 2.09228E+13
17 3.55687E+14
18 6.40237E+15
19 1.21645E+17
20 2.4329E+18
21 5.10909E+19
22 1.124E+21
23 2.5852E+22
24 6.20448E+23
25 1.55112E+25
26 4.03291E+26
27 1.08889E+28
28 3.04888E+29
29 8.84176E+30
30 2.65253E+32
31 8.22284E+33
32 2.63131E+35
33 8.68332E+36
34 2.95233E+38
35 1.03331E+40
36 3.71993E+41
37 1.37638E+43
38 5.23023E+44
39 2.03979E+46
40 8.15915E+47
41 3.34525E+49
42 1.40501E+51
43 6.04153E+52
44 2.65827E+54
45 1.19622E+56
46 5.50262E+57
47 2.58623E+59
48 1.24139E+61
49 6.08282E+62
50 3.04E+64

the factorial of 50 is 30414093201713378043612608166064768844377641568960512000000000000

Aliprep · Answer

Thank you GMATWhiz, Bunuel, zhengdeji. Understood now. So you guys are better than excel

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The integer 50! ends in how many zeros?

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The integer 50! ends in how many zeros?

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