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Prime Factorization

A factorization is prime when all the factors are prime numbers (those which only have itself and 1 as factors).

For example,

2 X 4 and 2 X 2 X 2 are both factorizations of 8. Only 2 X 2 X 2 is a prime factorization because 2 X 4 includes the composite number 4.

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Q: What makes the factorization of a number a prime factorization?
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Related questions

What makes a factorization of a number a prime factorization?

When all the factors are prime numbers, that's a prime factorization.


How do you write out the prime factorization of a prime number?

The prime number is the prime factorization. For example, the prime factorization of the prime number 3 is 3. Get it?


Is 53 prime factorization number?

53 is a prime number so there is no relevant prime factorization for it.


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The only number with that prime factorization has to be 48.


Can a number greater than 100 have only 1 number in it's prime factorization?

Yes. Any prime number greater than 100 has only itself in its prime factorization. Examples: The prime factorization of 101 is 101. The prime factorization of 109 is 109. The prime factorization of 127 is 127. The prime factorization of 311 is 311. The prime factorization of 691 is 691.


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91 cannot be in the prime factorization of any number because it is not a prime number itself.


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421 is a prime number so it does not have prime factorization.


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19 is a prime number, so it has no prime factorization.


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Since 89 is a prime number, the prime factorization of the number is simply 89.


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What is a diagram that shows the prime factorization of a number?

a prime factorization tree