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.

#NumberTheory #FundamentalTheoremOfArithmetic

Easy Math Editor

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Math	Appears 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

This factorisation is unique and apart from order.

Raisingh Mandloi - 5 years, 3 months ago

Math	Appears 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}`	$\boxed{123}$