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Source: — Problem Solving |
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by selango » Fri Jul 09, 2010 4:03 am
Number of 0's can be found by number of 10's

Number of 10's can be found by number of 5's

In 60! there are 12 5's(as 12*5=60).Also in 25 and 50 there are extra 2 5's.

So total 14 5's.
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by Rahul@gurome » Fri Jul 09, 2010 5:20 am
Zeroes as last digits in an integer are formed by the combination of 2 and 5. Every one pair will
combine as a product to give one zero.

60! has factors 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60.
25 will give two 5's and 50 = 25 × 2 = 5^2 × 2
They give 14 5's (As shown above, 25 and 50 both give 1 extra 5)

The correct answer is (C).
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by gmatinamonth » Sat Jul 10, 2010 12:20 pm
the question is basically asking what power of 10 can divide 60!.

When such a question comes, find out the prime factors of the divisor and note the highest prime factor ( in this case 5 as 5 will occur in 60! less than 2, thus determining the power of 10)

60/5 = 12

60/5^2 = 2

therefore, 12 + 2= 14 is the highest power of 5 in 60!
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by ankurmit » Mon Jul 12, 2010 11:49 pm
the question is basically asking what power of 10 can divide 60!.

When such a question comes, find out the prime factors of the divisor and note the highest prime factor ( in this case 5 as 5 will occur in 60! less than 2, thus determining the power of 10)

60/5 = 12

60/5^2 = 2

therefore, 12 + 2= 14 is the highest power of 5 in 60!

Thanks dear..

but i could not get why u wrote 60/5^2 = 2 ..means how you found it
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by kvcpk » Tue Jul 13, 2010 12:09 am
ankurmit wrote:
Thanks dear..

but i could not get why u wrote 60/5^2 = 2 ..means how you found it
Hi Ankurmit,

Its simple. As gmatinamonth says, just pick the largest of the prime factors.
In this case it is 5.

Now How do we get a 10? By multiplying 2 and 5.
If there are ten 2's and three 5's... How many 10's will I get?
Only 3. reason is I have only 3 5's that can multiply with 2.

For the same reason, we are trying to find how many 5's exist in 60!
You can remember this method blindly also.
We need to find the quotients in each of
60/5 + 60/(5^2) + 60/(5^3)+....
12+2+0...
=14

If we are asked in 200!,
it will be
200/5 + 200/25 + 200/125
=40+8+1 = 49

Hope this helps!!
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by ankurmit » Tue Jul 13, 2010 2:23 am
kvcpk..thanks..
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by ez2dj86 » Thu Jul 15, 2010 1:39 am
Try playing with other numbers too.

2 factorial = 2
3 factorial = 6
4 factorial = 24
5 factorial = 120
6 factorial = 720
7 factorial = 5040
8 factorial = 40320
9 factorial = 362880
10 factorial = 3628800
11 factorial = 39916800
12 factorial = 479001600
13 factorial = 6227020800
14 factorial = 87178291200
15 factorial = 1307674368000
16 factorial = 20922789888000
17 factorial = 355687428096000
18 factorial = 6402373705728000
19 factorial = 121645100408832000
20 factorial = 2432902008176640000
21 factorial = 51090942171709440000
22 factorial = 1124000727777607680000
23 factorial = 25852016738884976640000
24 factorial = 620448401733239439360000
25 factorial = 15511210043330985984000000
26 factorial = 403291461126605635584000000
27 factorial = 10888869450418352160768000000
28 factorial = 304888344611713860501504000000
29 factorial = 8841761993739701954543616000000
30 factorial = 265252859812191058636308480000000
31 factorial = 8222838654177922817725562880000000
32 factorial = 263130836933693530167218012160000000
33 factorial = 8683317618811886495518194401280000000
34 factorial = 295232799039604140847618609643520000000
35 factorial = 10333147966386144929666651337523200000000
36 factorial = 371993326789901217467999448150835200000000
37 factorial = 13763753091226345046315979581580902400000000
38 factorial = 523022617466601111760007224100074291200000000
39 factorial = 20397882081197443358640281739902897356800000000
40 factorial = 815915283247897734345611269596115894272000000000
41 factorial = 33452526613163807108170062053440751665152000000000
42 factorial = 1405006117752879898543142606244511569936384000000000
43 factorial = 60415263063373835637355132068513997507264512000000000
44 factorial = 2658271574788448768043625811014615890319638528000000000
45 factorial = 119622220865480194561963161495657715064383733760000000000
46 factorial = 5502622159812088949850305428800254892961651752960000000000
47 factorial = 258623241511168180642964355153611979969197632389120000000000
48 factorial = 12413915592536072670862289047373375038521486354677760000000000
49 factorial = 608281864034267560872252163321295376887552831379210240000000000
50 factorial = 30414093201713378043612608166064768844377641568960512000000000000
51 factorial = 1551118753287382280224243016469303211063259720016986112000000000000
52 factorial = 80658175170943878571660636856403766975289505440883277824000000000000
53 factorial = 4274883284060025564298013753389399649690343788366813724672000000000000
54 factorial = 230843697339241380472092742683027581083278564571807941132288000000000000
55 factorial = 12696403353658275925965100847566516959580321051449436762275840000000000000
56 factorial = 710998587804863451854045647463724949736497978881168458687447040000000000000
57 factorial = 40526919504877216755680601905432322134980384796226602145184481280000000000000
58 factorial = 2350561331282878571829474910515074683828862318181142924420699914240000000000000
59 factorial = 138683118545689835737939019720389406345902876772687432540821294940160000000000000
60 factorial = 8320987112741390144276341183223364380754172606361245952449277696409600000000000000
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