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Q: Is the prime factorization the same as the factor string?

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Yes.

Not really. A factor string is a multiplication sentence. A factor tree is a way of notating the process of finding the prime factorization of a given number. End result: 4 x 9 can be a factor string for 36, but can't be a prime factorization. The prime factorization of 36 is 2 x 2 x 3 x 3.

Yes.

567

Only if they're the same number.

Yes.

There are factor trees and ladders and rainbows and fireworks and they're all pretty much the same thing: ways to notate the process of finding the prime factorization of a given number. They differ in where they write the number and where the factors end up. In a factor tree, write the original number at the top and the bottommost branch will be the prime factorization. In a factor rainbow, write the original number at the bottom and the prime factorization will be the uppermost arc.

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.

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

2 x 5 x 5 = 50 satisfies those conditions.

No. Every composite number has one unique prime factorization. You can write it with or without exponents, but it's still the same prime factorization.

Prime numbers only have one prime factor. Prime factorizations have at least two. Sometimes they're the same number (2 x 2 = 4) so we could say it has one distinct prime factor.

No.

The prime factorization of fifty is 2x5^2 which is the same as 2 times 5 to the second power.

One way to find the prime factorization of a number is to start with the lowest prime number and see if it evenly divides the number. If it does, check whether the result of the division is divisible by that same prime number. When the prime number you are testing does not evenly divide that number, continue with the next prime number. Continue this until the result of the division is a prime number.Check whether 34 is divisible by 2:34 ÷ 2 = 1717 is a prime number, so the prime factorization is finished.The prime factorization of 34 is 2 x 17.Another way to find the prime factorization of a number is to choose a factor pair for that number. Then, find a factor pair for each of those numbers that is not prime.A factor tree of 34 is34/ \2 17Both 2 and 17 are prime, so the tree is finished.The prime factorization of 34 is 2 x 17.

Factor trees, ladders, rainbows, fireworks... They're all the same thing; ways of displaying the prime factorization of a given number. The prime factorization of 28 is 2 x 2 x 7. Write it however you wish. 7,2,2 14,2 28

No. The prime factorization of 100 is 2 x 2 x 5 x 5.

well becouse seens 72 has a lot of factors so it has to be the same becouse 72 is a prime number and it could be by the essact number.

No.

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.

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

The prime factorization of a number uses only primes. Ex: The prime factorization of 12 is not 6 x 2, and not 4 x 3, because 6 and 4 are not prime numbers. The prime factorization is 2 x 2 x 3. Their product is 12 and all factors are prime numbers. To get a prime factorization you are usually taught to factor through division by small prime numbers, sometimes you must use the same number more than once as in the example of 12 above 2 was used twice. Ex: find the prime factorization of 18. The smallest prime is 2... divide by 2 18 / 2 = 9 .... for the next step divide 9 by a prime 9 / 3 = 3 ... this is a prme ... it is also a factor so the prime factorization is 18 = 2x3x3 Ex. find the prime factorization of 35. 35 cannot be divided by 2, or 3, so use 5 first 35 / 5 = 7 .... since 7 is a prime we are finished. The prime factorization of 35 is 35 = 5 x 7 Some teachers teach this using a "factor tree" .. I can't type one of those on a computer.

19*5 this answer is also the same in exponent form.The prime factorization of 95 is 5*19.5 x 19 = 95

A factor rainbow, like factor trees, ladders, fireworks, lattices and cakes is a way to notate the process of finding the prime factorization of a given number. The process remains the same. If you would like to found a new method, just figure out a different way to write the numbers on the page.

There are factor trees, fireworks and rainbows, but these are just different ways of notating the same process. There are also ladders and continuous division.