Latest TCS Aptitude Question SOLUTION: Find the number of powers of 20 in 100! (a) 24 (b) 12 (b)1 (d)55

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Find the number of powers of 20 in 100!
(a) 24 (b) 12 (b)1 (d)55

Asked In TCS naresh (11 years ago)

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akshay sharma  (11 years ago)

ans is a) 24
20 is = 4*5 = 2^2 * 5
so we will look for no. of 2's and 5's in 100!.
no of 5's are= 24
np of 2's are=97, np of 4's are = 48
restrcting to the smaller quantity ans :24

Is this solution Helpfull? Yes (19) | No (4)  

Aastha  (11 years ago)

Keep on dividing 100 by 2.. find the maximum power of 2 in 100!
100/2=50, 50/2=25, 25/2= 12, 12/2=6, 6/2=3, 3/2=1, therefore total=50+25+12+6+3+1=97
Similarly for power of 5
100/5=20, 20/5=4 total=20+4=24
now factors of 20= 2*2*55
Power of 5=24, Power of 2=24+24=48
Therefore, power of 20=24

Is this solution Helpfull? Yes (7) | No (1)  

nidhi jain  (11 years ago)

20 = 5 * 4
thus the no. of times 5 & 4 will appear in 100! will be the power of 20 in 100!..
but it is well understood that no. of 5's are always lesser than 4 in 100! ...
thus we only need to calculate no. of 5's...
= (100/5)+(100/25)
=20+4
=24 is d power of 20.

Is this solution Helpfull? Yes (3) | No (1)  

Premkumar  (11 years ago)

Explain Properly.......I didn't understand...!

Is this solution Helpfull? Yes (2) | No (3)  

Lovejeet Singh  (11 years ago)

Plzzz xplain !!!

Is this solution Helpfull? Yes (2) | No (3)  

Swati  (11 years ago)

itz not just 100..itz 100 factorial(100!).

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