Unique Factorization Property

Question

Every Composite number can be factorised into primes in only one way,except, for the order of primes.

Except for the Order of Primes?? Please Clarify!

score 1 · Answer 1 · answered Sep 19 '15 at 12:28

1

It just means that $6=2\cdot 3$ and $6=3\cdot 2$ are not considered different factorisations.

answered Sep 19 '15 at 12:28

Sonner

3,108

Thanx Sonner, :-) – Amit Jha Sep 20 '15 at 01:06

score 1 · Answer 2 · answered Sep 19 '15 at 12:29

Consider the number $6$. When we say that it has a unique factorization into primes, we mean that $6 = 2\times 3$, and there is no other decomposition of $6$ into primes. However, I could have written $6=3\times 2$, reordering the primes which make up $6$. The property says that if we view these two factorizations as being the same (since we don't care about the order in which the primes are multiplied), then indeed the factorization of $6$ into primes is unique.

Thanx Alex, It was really helpful!! :-) – Amit Jha Sep 20 '15 at 01:05 — Amit Jha, Sep 20 '15 at 01:05

Unique Factorization Property

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