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(#M40039739) M4MATHS Category question Keep an EYE

what is the power of 20 in 100 factorial?

Asked In M4maths sachin prakash (10 years ago)

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BHASKAR MANDAL  (10 years ago)

the previous answer is wrong......
for this we have to calculate the prime factors of 20 = 5*2*2
highest prime factor is 5, so the no. of power of 20 will be depend on power of 5
so power of 5
100/5 = 20
100/25 = 4

so the power of 5 will be 20+4 = 24
and => power of 20 = 24

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BHASKAR MANDAL  (10 years ago)

100! = 100 *99*98*97......
so here multiples of 20 are 20,40,60,80and 100
so the power of 20 will be 5
20^5

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ARKA DAS  (10 years ago)

100/20=5 ans

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Mohammad Asif  (10 years ago)

prime factors of 20 are=2^2*5
100/5=20
20/5=4
4/5=0(taking only the quotient)
adding all these i.e. 20+4=24
now for prime factor 2
100/2=25
25/2=12 (25/2=12.5 but ignore the decimal)
12/2=6
6/2=3
3/2=1
1/2=0
adding all these i.e.(25+12+6+3+1=47)
47/2=23
since 23

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