Yesterday in class we learned about primes and composites, greatest common factor (GCF), and prime factorization.

Primes and Composites

-Primes can only be divided by 1 and itself.
-Composites can be divided by more than 2 numbers
-1 is not a prime or a composite because it can ONLY be divided by 1
-Some examples of prime numbers are 2,5,7,11
-Some examples of composites are 4,6,9,12

Prime Factorization

-Prime factorization is a composite number written as the product of its prime factors
-Divide by prime numbers starting with 2

Example: Find the prime factorization of 18. To start you would divide 18 by 2 and get 9. The next step is to break 9 down even more. Since 9 is not divisible by 2 you go to the next prime number which would be 3. Then 9 divided by 3 equals 3. Last step is to put the two numbers we divided by and the end result next to each other. So the prime factorization of 18 would be 2*3*3.

How to Find GCF


To find greatest common factor you first have to find the prime factorization of the first number. Then you need to find the prime factorization for the second number. Then you make a compare the two numbers' prime factorizations. (To make this easier, you could make a venn diagram). the factors that are the same are the ones you are looking for. The highest common factor is your GCF.

Example: Find the greatest common factor of 16 and 28. to start you would find the prime factorization of the two numbers. The prime factorization of 16 is 2*2*2*2. The prime factorization of 28 is 2*2*7. you next compare the two prime factorizations. Seven is the greatest out of the two of them but since 7 is not in the prime factorization of 16, then it can't be the GCF. The only other common factor is 2 so that is the GCF. The greatest common factor of 16 and 28 is 2.