Math 7 (Period 4)

Factoring Numbers & Expressions 5.1

A Prime number has exactly two factors—itself and 1

A whole number greater than 1 that has factors other than 1 and itself is called a composite number.

The number 1 is neither prime nor composite

Zero is neither prime nor composite.

You can use factor tress to find the prime factorization

and we found that there were many ways to use factor trees to arrive at the same prime factorization

So multiple Factor Trees could result in how you factor out number.

The product of prime numbers is called the prime factorization of that number.

You can also use something a called INVERTED DIVISION. It is similar to Factor Trees but you must begin with the smallest  prime factor that goes into the number and keep using it until it no longer works. Then go to the next higher prime factor… and keep going…

No matter which method you use,
you MUST write your PRIME FACTORIZATION from the smallest prime number to the biggest prime number.

54= 2∙3∙3∙3 That’s in expanded notation

54 =2∙3³ That’s in exponent notation

Negative numbers can be factored by using (-1) as a factor

What happens with variables?

-63a³ becomes (-1)∙3∙3∙7∙a³= (-1)∙3∙3∙7∙a∙a∙a

-27r3s = (-1)∙3∙3∙3∙r∙r∙r∙s

We could use exponents and when asked for prime factorization using exponential notation it would be:

(-1)∙3³∙r³∙s