Prime Factorization

Prime Factorization

Prime Numbers: they only have 2 factors...the number itself and 1.

2 is the only EVEN Prime Number...it's also the smallest Prime Number

0 and 1 are NOT Prime...neutral.

Composite Numbers: not Prime

Exponents:

3^{2 = 3x3 = 9........it is NOT 3 x 2 = 6}

^

Step 1: choose a factor pair (use mult. chart)

Step 2: always circle any factor that is PRIME

Step 3: draw a tree branch under composite number and list another factor pair for that number

Step 4: continue this until you have only PRIME numbers

okay....let's practice. Get out paper and pencil.

Find the Prime Factorization for 420

What factor pair will you choose?

Circle any numbers that are Prime.

Branch off of the Composite numbers...new factor pairs...circle prime numbers...continue on.

Prime Factorization = ?

List numbers in numerical order.

so...... 420

I am using 42 x 10

Branching off the 42 and 10

42 = 6x7 Circle 7 because it's prime

Branch off of the 6 =2 x 3 . Circle both 2 and 3

Now branch off the 10 = 2 x 5 Circle both the 2 and 5

Prime Factorization of 420 = 2x2x3x5x7

exponent:

2^{2 x 3 x 5 x 7}

^

Now find the Prime Factorization for 140.

Draw the Tree Diagram for 140...circle all prime numbers !

140 =2 x 2 x 5 x 7

140 = now with an exponent

2^{2 x 5 x 7}