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Q: How many prime factorizations does each number have?

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i believe, there can only be one.

The prime factorization of 1000 is 2 X 2 X 2 X 5 X 5 X 5

There are three numbers that fit those requirements.

A prime number has only two factors which are itself and one

There are many ways to find the LCM, or least common multiple. One way I like is to factor the number into primes first. So 5 is prime already and 25 is 5^2, and 30 is 5x3x2. Now take the largest value of each prime occurring in any of the prime factorization. So, for example, if we have 5, 5^2 and 5^3, in the three prime factorizations, we take the 5^3. If we do not see the prime at all, that is the same as p^0 which is 1. So In the example you asked about, we have 5^2x2x3=150. We can find the gcd in a similar manner by taking looking at the smallest exponent instead of the largest! Dr. Chuck

Related questions

An unlimited number.

Just one.

Every prime number has exactly 2 factors, 1 and the number itself.

At least two.

i believe, there can only be one.

Each number only has one prime factorization.

There are infinitely many possible answers. One such is 1001 = 7*11*13

To solve prime factorizations, divide a composite number by prime numbers until all the factors are prime. Many people like to use a chart of some kind to help visualize the process. One kind is a factor tree. Example: 210 210 Divide by two. 105,2 Divide by three. 35,3,2 Divide by five. 7,5,3,2 Stop. 2 x 3 x 5 x 7 is the prime factorization of 210.

Divide it by each prime number which does not have remainder.

The prime factorization of 1000 is 2 X 2 X 2 X 5 X 5 X 5

Each composite number has one distinct prime factorization. 26 = 64

Prime numbers have as factors the number 1 and their own number. Example: 37 is a prime number because its only factors are "1" and "37". If the prime number had further factors, it would no longer be prime.