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Q: Can two numbers have the same prime factorization?

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No.

Once your prime factorization is complete and you discover that there are no numbers in common, the GCF is one and the numbers are declared to be relatively prime.

Two.

The LCM of the given two numbers using prime factorization is 36

Two.

The prime factorization of 14 is 2 x 7. Prime factorization is multiplying two prime numbers by each other to get the original number.

567

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

Most of the time. If you can recognize that the two numbers are relatively prime, factorization isn't necessary. Just multiply the two numbers together.

If the prime factorizations have no prime factors in common, the numbers are relatively prime.

no. Prime numbers have to have two, and only two, factors: 1 and itself.

Use two factor trees.

102 has three different prime factors so there are no TWO numbers as required by the question.

30 and 42

30 and 60

Two is already prime. No factorization.

No.

Use the prime factorizations to determine the GCF. If the GCF is 1, the numbers are relatively prime. If the two numbers have no prime factors in common, they are relatively prime.

There are no two prime numbers that equal 960 when multiplied together. Prime factorization of 960 is 2x2x2x2x2x2x3x5 or 26x3x5.

The prime factorization of 243 will require 5 numbers. It is possible to write a factorization in two numbers, but they won't both be prime. 3 x 3 x 3 x 3 x 3 = 243 9 x 27 = 243

If the prime factorizations contain no factors in common (their GCF is 1), the numbers are relatively prime.

The prime factorization of 58 is: 2 x 29, so 2 and 29 are the two prime numbers that equal 58.

2 and 3

2 x 5 x 5 = 50 satisfies those conditions.

2 is already prime, no factorization is required.