Question

Find the no of zeros in 255 factorial + 88 factorial
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Answer 1

Answer:

83

Step-by-step explanation:

255! + 88! (no. of 0 depend on the no. of 5 and 2 )

Highest power of 2 in 255! :

255/2 + 255/4 + 255/8 + 255/16 + 255/32 + 255/64  + 255/128

127 + 63 + 31 + 15 + 7 + 3 + 1 = 247

Highest power of 5 in 255! :

255/5 + 255/25 + 255/125

51 + 10 + 2 = 63

So the no. of 0's in 255! is 63

Highest power of 2 in 88! :

88/2 + 88/4 + 88/8 + 88/16 + 88/32 + 88/64

44 + 22 + 11 + 5 +2 + 1 = 85

Highest power of 5 in 255! :

88/5 + 88/25

17 + 3 = 20

So the no. of 0's in 88! is 20

So the number of 0's in 255! + 88! = 63 + 20 = 83

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