Question

If N= 12^3 x 3^4 x 5^2 , find the total number of even factor of N.

Answer 1

@RaineJones @funinabox

Answer 2

Firstly we simplify the question so that all we get is N in terms of prime factors.

From here, we get N = 2^6 x 3^7 x 5^2

Then, we look at the prime factors.

To get an even factor, we must have a 2 in the factor.

(7+1) x (2+1) = 24

The number of types of 2s we can get is 6, since we can have 2^1, 2^2, .... etc. till 2^6.

Thus from here we get 24 x 6 number of even factors.

Therefore N has 144 even factors.

Hope this helped! Have a nice day :)

Answer 3

ok thanks for it

Answer 4

you're welcome :)