Factoring factors!

Find the number of even factors in 84000.


The answer is 80.

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1 solution

First, you have to factorize 84000, then you will get 2 5 . 3. 5 3 . 7 2^{5} .3.5^{3} .7 From those numbers, you can calculate the number of 84000's factor like this: ( 5 + 1 ) × ( 1 + 1 ) × ( 3 + 1 ) × ( 1 + 1 ) = 96 (5+1)\times(1+1)\times(3+1)\times(1+1) = 96 They added by 1 because n 0 = 1 n^{0} =1 and 1 is also the factor.

Even number is all numbers that are multiples of 2. So you have to include 2 at least 1.

( 5 ) × ( 1 + 1 ) × ( 3 + 1 ) × ( 1 + 1 ) = 80. (5)\times(1+1)\times(3+1)\times(1+1) = 80.

I did it the same way :)

Abhiram Rao - 5 years ago

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