Last updated April 10, 2022

Status: Tags: #archivedCards/macm101/numbertheory Links: Prime Numbers

Fundamental Theorem of Arithmetic

Theorems

Every integer n>1 can be represnted as a product of primes uniquely, up to the order of the primes ? Existence, by contradiction, suppose there is an n>1 that cannot be represented as a product of primes, and let m be the smallest such number

• m is not prime, therefore m = st for some s and t
• But then s and t can be written as products of primes, since $s<m$, and $t<m$ and they are less than the proven smallest number that cannot be represented as a product of primes

Examples

Find prime factorization of 980,220 ?

• Keep finding prime numbers it is divisible by

Backlinks

1

list from Fundamental Theorem of Arithmetic AND !outgoing(Fundamental Theorem of Arithmetic)

References:

Created:: 2021-11-29 20:24