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Prime Factorization

"Prime Factorization" is finding which prime numbers you need to multiply together to get the original number.

Example 1

What are the prime factors of 12?

It is best to start working from the smallest Prime number, which is 2, so let's check:

12 ÷ 2 = 6

But 6 is not a prime number, so we need to factor it further:

6 ÷ 2 = 3

And 3 is a prime number, so:

12 = 2 × 2 × 3

As you can see, every factor is a prime number, so the answer must be right - the prime factorization of 12 is 2 × 2 × 3, which can also be written as 22 × 3

Example 2

What is the prime factorization of 147?

Can we divide 147 evenly by 2? No, so we should try the next prime number, 3:

147 ÷ 3 = 49

Then we try factoring 49, and find that 7 is the smallest prime number that works:

49 ÷ 7 = 7

And that is as far as we need to go, because all the factors are prime numbers.

147 = 3 × 7 × 7 = 3 × 72

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Q: How do you find the prime factorization of any number?

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I find the easiest way to find the prime factorization of any number is to start with the smallest prime number that divides the number. So, for 50, I would start with 2. Now we have 2x25. Since 25 is 52 we find the prime factorization of 50 is 2x5x5.

91 cannot be in the prime factorization of any number because it is not a prime number itself.

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

Prime factorization never includes a composite number. All numbers in prime factorization must be prime numbers.

First, find the prime factorization of the number. For instance, with 45: 45 = 3 * 3 * 5 = 32 * 51 Now, from this prime factorization, any numbers whose prime factorizations do not include these factors is coprime to the number you have.

Any number that isn't prime.

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.

Every composite number has its own unique prime factorization.

Any of the prime numbers will fit this description

The number 37 is already prime so it can't be factored into primes any further.

Use a factor tree. 343 49,7 7,7,7

Any power of 2

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.

To find the prime factorization of a number, start with any factor pair of that number and keep factoring the composite numbers until all factors are prime. 55 5 x 11 = 55 Both factors are prime, so that is the prime factorization.

No. Any factor string of a negative number would have to include at least one negative number and there aren't any negative prime numbers.

No. Any factor string of a negative number would have to include at least one negative number and there aren't any negative prime numbers.

Write the prime factorization with exponents. Add 1 to each exponent. (Numbers without exponents actually have the exponent 1.) Multiply them together. That will be the number of factors.

If the number is even, there will be at least one 2 in the prime factorization. If the number is odd, there won't be any twos.

Not Prime Factorization1 is not the prime factorization of 36. To find the prime factorization of 36, start with any two factors:2 X 18 = 36Then, continue to factor any number in the equation that can be factored:2 X 2 X 9 = 362 X 2 X 3 X 3 = 36When you can no longer factor any number in the equation, you have the prime factorization, so the prime factorization of 36 is 2 X 2 X 3 X 3.

Prime factorization is the result of expressing a number as the product of its prime factors. It will assist you in finding the GCF and LCM of any given number set.

Any prime number raised to a power.

Prime factorization is a common mathematical tool. One uses prime factorization to determine what prime factors of any given number are. One can practice this tool online.

Since the number 10 has the prime factorization of 2 x 5, any multiple of 10 has the numbers 2 and 5 in their prime factorization.

Finding the Prime Factorization of 66To find the prime factorization of 66, find the lowest prime number that will divide evenly into 66. Since 66 is an even number, that number will be 2. Find the number which when multiplied by 2 equals 66. The number is 33. Write it down like this:2 X 33 = 662 is one of the prime factors of 66, but 33 is a composite number and must be factored. Find the lowest prime number that divides evenly into 33. The number cannot be 2 because 33 is an odd number. 3 is the lowest prime number that will divide evenly into 33. The number that when multiplied by 3 equals 33 is 11. Write it like this, keeping the 2 from the previous factorization:2 X 3 X 11All the factors are now prime numbers, so the prime factorization of 66 is:2 X 3 X 11This is one method that works for finding the prime factorization of any composite number.

0, 1 or any composite number