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Source: — Problem Solving |

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by Anurag@Gurome » Sun Jan 29, 2012 12:01 am
sud21 wrote:A number is the product of integers from 1 to 10. How many zero are in the number?
The number of zeroes at the end of an integer depends upon the number of 10s in its factor. Which n turn depends upon number of 2s and 5s.

Now in the product of all the integers from 1 to 10, there will be more 2s than 5s. Hence, number of 5s will determine the number of 10s.

Number of 5 in all the integers from 1 to 10 = 2 (one in 5 itself and another one in 10)

Hence, there will two zeroes at the end of the product.
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by Abhishek009 » Sun Jan 29, 2012 9:49 am
sud21 wrote:A number is the product of integers from 1 to 10. How many zero are in the number?
Product of 1 to 10 means 10!

Now find the total number of 5'd in it -

10/5 => 2

So there will b 2 zero's in the end..
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by ronnie1985 » Sun Jan 29, 2012 10:14 am
10 = 2*5. hence we have to count the no of 5s in the product of 1 to 10 which can be done by adding the maximum exponent of 5 in 10!
=[10/5]+[10/25] = 2+0 = 2. here [x] is greatest integer function less than or equal to x.

For questions of finding the maximum power of x to which a given no can be divided, we take the same approach as given here.
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