Here's one possibilty.....assume all the numbers are integers...one of the numbers must be 5 because a product ending in 5 must have a factor of 5
Dividing 585 / 5 = 117
And 117 can be written as 9 * 13 .......so
Let
a = 5, b = 9, c =13
a + b + c = 5 + 9 + 13 = 27
a*b*c = 5 * 9 * 13 = 585