Prime Numbers

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

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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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## Related Questions

1 is not a prime number, so it wouldn't be present in any prime factorization. Prime numbers don't really have factorizations, that is, the factorization is the number itself. There are prime numbers greater than 100.

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

No. Prime numbers (of any size) have only one prime factor, but that's not really a factorization.

There is no factorization. 37 is a prime number.37 is already prime. Its only prime factor is itself.

5 is a prime number. It is only evenly divisible by itself and one.5 is a prime number, so the only prime factor of 5 is itself.5 is already a prime number; it has no factorization.

There is only one prime factorization string for each number, so there is not a "longest" one. Since 239 is a prime number, its prime factorization is 239.

Every positive composite number only has one unique prime factorization.

11 is a prime number. Its only prime factor is 11.

There is no prime factorization of 47 since it is a prime number. It's only factors are 1 and 47.

Because 100 only has one prime factorization.Because each composite whole number has a unique prime factorization.

All even numbers contain the number 2 in their prime factorization, as 2 is the smallest prime number and the only even prime number.

Only if they're the same number. Every composite number has a unique prime factorization.

The prime factorization of 64 is 2x2x2x2x2x2 or 26. 2 is the only prime number in the factorization of 64.

Every positive composite number only has one unique prime factorization.

23 is a prime number and its only prime factor is 23.

359 is a prime number. Its only prime factor is 359.

233,357 is a prime number. Its only factors are 1, 233357

67 is a prime number and is consequently only divisible by 1 and itself.67 is already prime; no need for a factorization.

In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integergreater than 1 either is prime itself or is the product of prime numbers, and that this product is unique, up to the order of the factors.

7 is a prime number and therefore its only prime factor is itself.

Saying "The" Instead of "A"The prime factorization is used instead of a prime factorization because there is only one correct prime factorization of any given number. Of course, that refers to composite numbers because prime numbers have no prime factorization.The use of the word "a" implies that more than one prime factorization is possible when it's not. The use of the word "the" signifies that only one prime factorization is possible, though there are various ways to arrive at it.

1,0012 = 1,002,001. The prime factorization of 1,002,001 is:None! 1,002,001 is a prime number. Its only factors are 1 and 1,002,001.

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