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

a) 3.

b) 4.

c) 5.

d) 6.

e) 10.

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.

Step 2 ;

(b) Given that n=4

Number 5 contain only 2 factor

So 6 contain 4 factor such has 1,2,3,6.

Hence ,

The smallest positive integer with factor 4 is 6.

Step 3 :

© Given that n=5

Since the number 16 contain 5 factor such has 1,2,4,8 and 16.

Hence ,

The smallest positive integer with factor 5 is 16.