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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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Factoring and Multiples

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What is the prime factorization of 24

What is the prime factorization of 54

What is the prime factorization of 64

What is the prime factorization of 34

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

What is the prime factorization for the number 50?

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.


How do you know without dividing that 91 is not in the prime factorization of 75257?

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


Describe a way to find the prime factorization of any whole number?

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


Does the prime factorization of any composite number include prime and composite numbers?

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


How do you find coprimes of a number?

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.


What number never appears in a prime factorization?

Any number that isn't prime.


Can a number greater than 100 have only 1 number in it's prime factorization?

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.


Does any other number have the prime factorization 13 and 30?

Every composite number has its own unique prime factorization.


What number has prime factorization with 1 prime number?

Any of the prime numbers will fit this description


How do you find the prime factorization of 37?

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


How do you find the prime factorization of 343 or any number?

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


A number with the only prime number in its prime factorization that's 2?

Any power of 2


Can a number over 100 only have 1 in its prime factorization?

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.


How do you prime 55?

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.


Is it possible to find the prime factorization of a negative number and how do you do it?

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.


Is it possible to find the prime factorization of a negative number?

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.


Will prime factorization help find the number of factors of any number?

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.


How can the prime factorization of a number help you determine if the number is even or odd?

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.


Is 1 the prime factorization of 36?

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.


What is the definition and purpose of prime factorization?

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.


Which numbers have a prime factorization that are all equal?

Any prime number raised to a power.


How does the prime factorization of numbers work?

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.


What numbers have 2 and 5 in their prime factorization?

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.


How do you get the prime factorization of 60?

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.


Which number never appears in a prime factorization?

0, 1 or any composite number