+0

In how many zeros does 75! end? (Note that is the product of the first positive integers; for example, .)

0
626
1
+416

In how many zeros does 75! end? (Note that  is the product of the first  positive integers; for example, .)

Dabae  Jul 7, 2015

#1
+82733
+10

There is an algorithm for this.....

Note that a zero is added everytime a "5" is multiplied by an even number....so....we just need to find the number of 5s that are multiplied in 75!

Divide 75 by 5 =   15

Divide 75 by 5^2   =   75  / 25   = 3

Then...there are 15 + 3  = 18  "5s" that are multiplied together in 75!......and we have more than enough even numbers to pair each 5 with....so......

Add 15 + 3     = 18 trailing zeros

CPhill  Jul 7, 2015
Sort:

#1
+82733
+10

There is an algorithm for this.....

Note that a zero is added everytime a "5" is multiplied by an even number....so....we just need to find the number of 5s that are multiplied in 75!

Divide 75 by 5 =   15

Divide 75 by 5^2   =   75  / 25   = 3

Then...there are 15 + 3  = 18  "5s" that are multiplied together in 75!......and we have more than enough even numbers to pair each 5 with....so......

Add 15 + 3     = 18 trailing zeros

CPhill  Jul 7, 2015

16 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details