Number Theory least divisor of integer is prime number if integer is not prime

[teddyayalew]

Homework Statement

The question is not really a question from a book but rather a statement that it makes : it says " Obviously the least divisor[excluding 1] of an integer a is prime if a itself is not prime." I kind of believe this statement but I'm having trouble proving the general case

Homework Equations

The Attempt at a Solution

when I take a few examples : a =8 , 2 (LD) is prime . a = 10, 2(LD) . a = 9, 3(LD) is prime a =121, 11(LD) is prime. But I'm having trouble generalizing this for all n.

 

[sunjin09]

any non-prime divisor can be further divided.

 

[teddyayalew]

Thank you! I feel stupid but happy I understand now.