How many numbers that are not divisible by 6 divide evenly into 264,600?
(A) 9
(B) 36
(C) 51
(D) 63
(E) 72
how we can do this one quickly
(A) 9
(B) 36
(C) 51
(D) 63
(E) 72
how we can do this one quickly
(prime factors) of 264,600 = 2^3 * 3^3 * 5^2 *7^2
Numbers that will divide 264600 and that are not divisible by 6. will be the factors which contain only 2,5,7 and 3,5,7
number of factors= (3+1)(3+1)(2+1)(2+1)=144
now 2*3=6----> all factors where 2*3 is a part of factor will be divided by 6
there are 3 two's and 3 three's----->number of factors which contain 2 and 3 is 3*3=9
now when these no's r mutliplied to 5 and 7 we have to multiply 9 by (2+1)*(2+1)=9 (powers of 5 and 7 plus 1) --> 9*9=81 no's which are divisible by 6 so ---> 144-81=63. is the reqd no.
oooffff!!!!!!!
it took me 15 mins....IMO D
and on the exam day i wud have guessed after a max of 2 min
eager to c any shorter approach
