Waste less time on Facebook — follow Brilliant.

The Fundamental Theorem of Arithmetic

The Fundamental Theorem of Arithmetic is the easiest of the 3, but it isn't as fundamental as you think it is. It states that every number can be prime factorized uniquely as a product of primes. No 2 numbers have the same prime factorization, and no number has 2 distinct prime factorizations.

For instance, \(10=2\times5\).

\(10\) cannot be represented as another distinct prime factorizations and no other number is prime factorized into \(2\times5\).

You are welcome to prove it in the comments below.

Note by Aloysius Ng
2 years, 1 month ago

No vote yet
1 vote


Sort by:

Top Newest

This factorisation is unique and apart from order. Raisingh Mandloi · 10 months, 3 weeks ago

Log in to reply


Problem Loading...

Note Loading...

Set Loading...