You Want What Is The Sum?

Number Theory Level 1

Find the sum of the last 17 digits of 100 ! 100! .


The answer is 0.

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Shithil Islam by shithil Islam , 18, Bangladesh

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5 solutions

Shithil Islam
Feb 6, 2016

We know the last 24 digit of 100! is 0 . So, the answer is 0.

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I am not understanding. How is knowing that the last digit is 0 help you with the sum?

Jonah Burian - 5 years, 4 months ago

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The last 24 digits are 0

Arulx Z - 5 years, 2 months ago

is he asking sum or product?

Kaleem Kħặŋ - 5 years, 4 months ago

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I am asking sum. If the last 24 digit of 100! is 0, then the sum of last 17 digit is definately 0.

shithil Islam - 5 years, 4 months ago

Number of trailing zeroes in 100 ! = ⌊ 100 5 ⌋ + ⌊ 100 25 ⌋ = 24 \text{Number of trailing zeroes in} \;100!=\lfloor\frac{100}{5}\rfloor+\lfloor\frac{100}{25}\rfloor=\boxed{24} For those unfamiliar with how I calculated the trailing number of zeroes, you may want to see the relevant wiki

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Jase Jason
Mar 24, 2016

Oh, I thought it was all the numbers. I said 0...00(17 0's)

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Aman Dubey
Feb 15, 2016

We know that 100! Is equal to 1 2 3 4... 99 100 Thus no of zeroes can be determined by number of multiple of 10. Multiple of 10 are 2 5, 10, 15*4, 20... Thus there are 24 such zeroes

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Sry i need to learn latex

Aman Dubey - 5 years, 4 months ago
Sunil Pradhan
Feb 6, 2016

To find number of zeroes in 100!

100/5 = 20

20/5 = 4

Total number of zeroes = 20 + 4 = 24

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Yes , you are absilutely right..........

shithil Islam - 5 years, 4 months ago

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