X, Y, and Z are three different Prime numbers, the product XYZ is divisible by how many different positive numbers?
Please describe method.
PRIME # is the # that has only 2 factors: One is 1 and another is the # itself.
FOR any given # 1 and the # iteself are the definite factors.
Knowing above conepts:
product of X,Y, and Z = XYZ
divisible by 1, xyz, x, y, z, xy,yz,xz ==> total 8
if question has 5 constants a,b,c,d,e, we do not have to count in the above way
Basically we are selecting, from the product, one constant, set of two constants, set of 3 constants ....and so on set of all the # of constants.
so if 5 varibales are given, total # ways to select is 5C1+5C2+5C3+5C4+5C5 = 5+10+10+5+1 = 31
And answer will be 31+1 =32 (as "1" is a factor for every #)