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

  • #1

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.
 

Answers and Replies

  • #2
312
0
any non-prime divisor can be further divided.
 
  • #3
Thank you! I feel stupid but happy I understand now.
 

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