determine how many zeros are at the end of the numerals for the following numbers.

a. 10!

b. 100!

c. 1000!

Printable View

- Mar 31st 2010, 09:36 AMihavvaquestionfactorial question
determine how many zeros are at the end of the numerals for the following numbers.

a. 10!

b. 100!

c. 1000! - Mar 31st 2010, 10:28 AMSoroban
Hello, ihavvaquestion!

Quote:

Determine how many zeros are at the end of the numerals for the following numbers.

. .

Every factor of 5 (combined with an even number) creates a final zero.

The question becomes: How many factors-of-5 are contained in ?

We know that: .

And every 5th number contains a factor-of-5: . factors-of-5

Therefore: . ends inzeros.*two*

Every 5th number contains a factor-of-5: . factors-of-5.

But every 25th number contains

Each contributes an additional factor-of-5: . more factors-of-5.

Therefore, ends in: . zeros.

Every fifth number contains a factor-of-5: . factors-of-5.

But every 25th number contains

Each contributes another factor-of-5: . more factors-of-5.

And every 125th number contains

Each contributes another factor-of-5: . more factors-of-5.

And every 625th number contains

Each contributes yet another factor-of-5" . more factor-of-5.

Therefore, ends in: . zeros.