according to the fundamental theorem of arithmetic (unique factorization theorem), you can write every number together the product of some prime numbers, for example \$33 = 11 cdot 3\$.

You are watching: Prime numbers can be written as a product of

However, how can you execute this once you"re managing a element number? If you compose \$29 = 29 cdot 1\$ you usage 1 and also that isn"t a prime number. Need to you simply write \$29 = 29^1\$?

A solitary number, like \$31\$ or \$7\$, is in fact a product as far as snucongo.orgematics is concerned. The is a product that \$1\$ integer.

Indeed, friend can even have a product of \$0\$ integers. This is identified to it is in \$1\$, since \$1\$ is the identity element of multiplication. (See Qiaochu"s comment.)

When us say the an integer has actually a distinctive prime factorization, we typical it can be written as a product of some nonnegative integer variety of primes. Thus, "\$2 cdot 2 cdot 23\$", "\$31\$", "\$7\$", and "\$quad\$" space all precious prime factorizations.

Thanks for contributing solution to snucongo.org Stack Exchange!

But avoid

Asking because that help, clarification, or responding to various other answers.Making statements based upon opinion; earlier them up with recommendations or an individual experience.

Use snucongo.orgJax to format equations. snucongo.orgJax reference.

See more: What Must Be True About An Index Fossil Whose Absolute Age Is Used As A Reference For Other Fossils

Not the price you're looking for? Browse various other questions tagged prime-numbers prime-factorization or ask your very own question.

What's the suggest of remove \$1\$ from the list of primes and having an empty product in the basic theorem the arithmetic?

site design / logo design © 2021 stack Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.11.23.40817

snucongo.orgematics ridge Exchange works finest with JavaScript permitted