can you find the number of zeros

Level 2

100 × 99 × 98 × ⋯ × 2 × 1 100\times99\times98\times\cdots\times2\times1

Find the number of zeros formed at the end of the above number.


The answer is 24.

Devansh Agarwal by devansh agarwal , 21, India

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1 solution

We are basically calculation how many (5 2) are there. there is no problem with 2 as there is a lot of even numbers in your range. 5 can be found on 5,10,15,20,30,... ... 65,70,80,... ...95 (excluding 25,50,75,100) only 1 time which makes it 16 times and we can get two fives from 25,50,75,100 each as there is a factor(5 5) in these 4 numbers. so the count stands 16 + 2*4 = 24

1 Helpful 0 Interesting 0 Brilliant 0 Confused

We know that multiple of 5 and 2 multiply together to produce a 0 but factor of 5 is less in 100! Is less than factor of 2 so factor of 5 is deciding in these two(2&5). So we can calculate multiple of 5 by using greatest integer function [100/5]+[100/(5^2)]+[100/(5^3)]+.....so on =20+4+0 =24

Arindam Tomar - 6 years, 10 months ago

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