Problem 46E

Find the smallest positive integer with exactly n different positive factors when n is

a) 3.

b) 4.

c) 5.

d) 6.

e) 10.

Solution :

Step 1 :

In this problem we have to find the smallest positive integer with n different positive factor.

Given the n values 3,4,5,6,10.

- Given that ,

1 contain only one factor,

2 and 3 contain only 2 factor,

Thus 4 contain 3 factor such has 1,2 and 4.

Hence ,

The smallest positive integer with factor 3 is 4.