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
3 years, 1 month ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

This factorisation is unique and apart from order.

Raisingh Mandloi - 1 year, 10 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...