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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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.
Prime factorization never includes a composite number. All numbers in prime factorization must be prime numbers.
Use a factor tree. 343 49,7 7,7,7
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.
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.