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Q: Can two different numbers have the same prime factorization?

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Yes.

No, multiplying a set of numbers can only come out as one product. Therefore, two numbers having the same prime factorization is impossible.

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

A prime factorization is the same as expressing a composite number as the product of its prime factors. Prime numbers don't have factorizations; they're already prime.

No.

Factor strings don't necessarily have to be composed entirely of prime numbers. But the longest factor string, the one that is entirely prime numbers, that's the prime factorization.

Usually, but not necessarily and not if they're prime. All prime numbers have the same number of factors.

Powers of primes

The same way as with smaller numbers, it may take longer. Just keep dividing by prime numbers until all the factors are prime.

No because all the numbers in a prime factorization must be prime. The number 9 is not prime. It should be 3 *3. same thing with 4, should be 2*2. So what would be a prime factorization is 2x2x2x3x3x5x11.

The same way as with smaller numbers, it may take longer. Just keep dividing by prime numbers until all the factors are prime.

Prime factorization of 115 is: 5x23 Prime factors are the prime numbers multiplied with each other that together form the original numerical value. Prime numbers are numbers that have no factors besides one and itself. The first prime number is 2, then 3, 5, 7, 11, 13, and so on. Sometimes one may have a number that has multiple same prime numbers for its prime factorization; for example the prime factorization of 256 is 2x2x2x2x2x2x2x2

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