Posted by failureinmath on .
What is the probability that a randomly selected divisor of 720 is a multiple of 4? Express your answer as a common fraction.

PLEASE HELP  DIVISORS PROB 
Steve,
since 720 = 4*180
and 180 = 2^2 3^2 5
180 has 18 factors:
1 2 4 6 12 18 36
10 20 30 60 90
3 9 15 45 180
I'd say 1/18, since all the factors that are multiples of 4 will be 4 times one of the factors in the list. 
PLEASE HELP  DIVISORS PROB 
geometrygeeeeek,
thanks alot

PLEASE HELP  DIVISORS PROB 
Jacob,
3/5

PLEASE HELP  DIVISORS PROB 
s,
15

PLEASE HELP  DIVISORS PROB 
Someone,
Using the above logic, the answer is 3/5.
All the reasoning is correct (About the factors of 180). The only problem is that the probability of selecting one. Since the prime factorization of 720 is 2^4 x 3^2 x 5, then the number of factors that 720 has is (4+1)(2+1)(1+1)=30. So, the answer is 18/30=3/5