Latest CTS Aptitude Question SOLUTION: Find the highest power of 10 in 203!

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(#M40026221) CTS Numerical Ability question Keep an EYE

Find the highest power of 10 in 203!

Asked In CTS keerthika manoharan (10 years ago)

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Rachna  (10 years ago)

10=2*5 (prime factors of 10)
highest power of 10 in 203!=min(power of 2 in 203!,power of 5 in 203!)

power of 2 in 203! = |203/2| + |203/4| + |203/8| + |203/16| + |203/32| + |203/64| + |203/128| =101 + 50 + 25 + 12 + 6 + 3 + 1= 198

power of 5 in 203! = |203/5| + |203/25| + |203/125|= 40 + 8 + 1 = 49
=> min( 198,49)=49

Is this solution Helpfull? Yes (47) | No (1)  

srinivasan  (10 years ago)

203/2 = 101
101/2 = 50
50/2 = 25
25/2 = 12
12/2 = 6
6/2 = 3
3/2 = 1
Hence the power of 2 in 203! = 101 + 50 + 25 + 12 + 6 + 3 + 1 = 198
Now let’s divide 203 with 5
203/5 = 40
40/5 = 8
8/5 = 1
Hence the power of 5 in 203! = 40 + 8 + 1 = 49
Therefore, the power of 10 in 203! is 49.

Is this solution Helpfull? Yes (31) | No (1)  

maithali  (10 years ago)

simplest method to obtain solution of the highest power in factorial of any no. is to divide it by 5 and keep dividing :
203/5= 40 ignore the remainder part
now 40/5= 8
now 8/5=1 just write the quotients
now add the quotients: 40+8+1=49

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manoj kumar  (9 years ago)

find no of zeros in 203!
that is49
203/5=40
40/5=8
8/5=1
40+8+1=49
48/2=24 and 1 10
10 power 25

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