Question

The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of K?(1) 3^2 is a factor of k(2) 7^2 is NOT a factor of k

Answer 1

k is 63

Explanation:

The positive integer k has exactly two positive prime factors, 3 and 7

Lets write the combination of prime factors including 1 and k

1, 3, 7, _ , _ , k

using the above factors 3 times 7 is also the factor

so 21 is the other factor

1, 3, 7, 21 , _ , k

Now we use the given statements

(1) 3^2 is a factor, so 9 is also a factor

1, 3, 7, 21 , 9 , k

7^2 is NOT a factor of k. so 49 is not a factor of k

So 3,3 and 7 is the factor of k

`3 \cdot 3 \cdot 7 \cdot = 63`

K is 63