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How many zeros are there at the end of the number which is the product of first hundred positive integers?

Trailing Zeros

Stage: 3 and 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

The symbol $50!$ represents the product of all the whole numbers from 1 to 50 inclusive; that is, $50!=1 \times 2 \times 3 \times \dots \times 49 \times 50$. If I were to calculate the actual value, how many zeros would the answer have at the end?

 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

 

 

This problem is taken from the UKMT Mathematical Challenges.

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