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how many zeros will be their in the end of 25!
Dear Shivam
0 is created by product of 2 and 5
if we can find the exponent of 2 and 5 in the expansion of 25! then it will give number of zero
exponent of prime number 2 in 25!= [25/2] + [25/22]+[25/23]+[25/24]+[25/25]+.......all zero , [] denotes greatest integer function here
=12+6+3+1+0... = 22
exponent of 5= [25/5] + [25/52]+[25/53]+0..... = 5+1+0.... = 6
so there are 6 pairs of 2 and 5 it will give rise to 6 zeros in the end
All the best.
AKASH GOYAL
AskiitiansExpert-IIT Delhi
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