AIEEE Discussion Forum, Questions

Counting is actually a fairly interesting and under-explored topic. Let us set the ball rolling with an interesting question from this topic.

Question: How many zeroes are there at the end of 50!
a. 12
b. 10
c. 8
d. 11

Cheers all,

Are all the answer choices correct?

I am getting an answer of 5.

10, 20, 30, 40 and 50 will have one 0 and the final product will have 5 0s.

Hi Mani,

I think you have made an interesting start. multiplying by 10 will definitely give one zero. But is this the only way to get a zero? Think about it. What is 5!?

For the record, the answer choices are correct .

It might be interesting to take this discussion forward by arriving at a nice method to find the number of zeroes in 50!

10 is the answer.

Missed the fact that product of 2 and 5 will result in a '0', should have accounted for 5, 15, 25, 35 and 45. These add another 5 more 0s.

Hi Mani,

Your approach is correct, but there is still one more step to go. 25 and 50 each contribute 2 5's to the product, so will give 2 zeroes to the factorial. 24! will have 4 zeroes, whereas 25! will have 6. So, the right answer is 10+2 = 12 zeroes.

Can you arrive at a generic formula for arriving at number of zeroes for n! from hereon.