2007 iTest Problems/Problem 34
Problem
Let 
be the probability that a randomly selected divisor of 
is a multiple of 
. If 
and 
are relatively prime positive integers, find 
.
Solution
The prime factorization of is 
, so has 
positive divisors. Of the six positive divisors, four of them are divisible by . Thus, the probability that a divisor is a multiple of is 
, so 
.
See Also
| 2007 iTest (Problems, Answer Key) | ||
| Preceded by: Problem 33 |
Followed by: Problem 35 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 • 51 • 52 • 53 • 54 • 55 • 56 • 57 • 58 • 59 • 60 • TB1 • TB2 • TB3 • TB4 | ||
