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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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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.
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 the prime factorization of 343 or any number?
Use a factor tree. 343 49,7 7,7,7
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.
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.
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.
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.
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.
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.
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.
What number has prime factorization with 1 prime number?
Any of the prime numbers will fit this description
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.
How do you find the prime factorization of 343 or any number?
Use a factor tree. 343 49,7 7,7,7
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.
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.
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.
