Positive Integer Greater than 1 has Prime Divisor/Proof 1

From ProofWiki
Jump to navigation Jump to search

Lemma

Every positive integer greater than $1$ has at least one divisor which is prime.


Proof

By the Fundamental Theorem of Arithmetic, every natural number greater than one can be factored into a unique set of prime numbers.

Therefore, every positive integer greater than one has at least one prime factor.

$\blacksquare$