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how many zeros will be their in the end of 25! how many zeros will be their in the end of 25!
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 Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation. Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian. Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar respectively : Click here to download the toolbar..
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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