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

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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 $29 = 29^1$?


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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.


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