PS- number prop 264 600

[Xbond]

Hi there,

could you help to understand and resolve this PS in the simplest way

How many numbers that are not divisible by 6 divide evenly into 264,600?

(A) 9
(B) 36
(C) 51
(D) 63
(E) 72

[real2008]

is that D?

[Xbond]

I would like your full explanation, please

[praky_rules]

264600 = 2^3 x 5^2 x 3^3 x 7^2

Total number of factors that are not divisible by 6 = Total number of factors - Total number of factors divisible by 6.

Total number of factors = (3+1) x (2+1) x (3+1) x (2+1) = 144 (For 2^3 term, you can pick "2" 3 times or not pick it at all = (3+1))

Total Number of factor divisible by 6 = you have to pick 2 atleast once and 3 atleast once. So total possible factors = 3 x (2+1) x 3 x (2+1)
= 81

144-81 = 63. Can I get a hug?