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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