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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
All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.
Example: 210
210 Divide by two.
105,2 Divide by three.
35,3,2 Divide by five.
7,5,3,2 Stop. All the factors are prime.
2 x 3 x 5 x 7 = 210
That's the prime factorization of 210.
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How are factors and prime numbers alike?
Some factors are prime numbers.
How are prime factors and factors related?
Prime factors are factors that are also prime numbers.
Will you get the same number of factors if you multiply a prime number and itself?
Prime numbers have two factors. Prime squares have three factors. Square numbers have an odd number of factors but that number varies.
How can you find the gcf of two numbers is 1by looking at their prime factorazations?
If they have no prime factors in common, their GCF is 1.
What is the answer of three numbers have 2 factors in math?
Prime numbers have two factors. 2, 3 and 5 are prime numbers.
How do you find out which one are the prime numbers?
Prime numbers have only two factors.
How do you work out the product of prime factors?
Multiply prime numbers or prime factors to find their product.
Which prime numbers can be mulitiplied to form?
Prime numbers are used to find the product of the prime factors of composite numbers.
What dose prime factor mean?
it means to find out if the number is composite or prime
What is the method to find the prime factors of a composite number?
prime numbers
How do you find prime factors fo a number?
List all the factors. Select the ones that are prime numbers.
What numbers or prime?
All numbers that only have one and itself as factors are prime. Therefore, to tell if a number is prime simply find it's factors. If it has more than two factors than it is not a prime number.
What prime numbers are prime number?
All numbers that only have one and itself as factors are prime. Therefore, to tell if a number is prime simply find it's factors. If it has more than two factors than it is not a prime number.
How do you find prime and composite numbers?
By factoring them. Prime numbers have only two factors. Composite numbers have three or more.
Which of the numbers is prime?
All numbers that only have one and itself as factors are prime. Therefore, to tell if a certain number is prime simply find it's factors. If it has more than two factors than it is not a prime number.
Is The of prime numbers?
All numbers that only have one and itself as factors are prime. Therefore, to tell if a certain number is prime simply find it's factors. If it has more than two factors than it is not a prime number.
What is the meaning of prime numbers and composite numbers?
All numbers that only have one and itself as factors are prime. Therefore, to tell if a number is prime simply find it's factors. If it has more than two factors than it is not a prime number, otherwise it is composite.
