Finding the GCF through Prime Factorization

Please read through as a refresher for tomorrow's lesson. We will be spending some more time on GCF.

Let's review how we can find the GCF of each set of numbers by using the prime factorization method. This example does NOT use exponents. I want to give you a visual of how to do it without turning your PF into exponent form juuuuuust in case you forget to use exponents.

1)  16, 60

First, find the prime factorization of each:

Next, identify the matches on each side. A "match" is when there's a number on one side (at the bottom of the tree) that has an EXACT twin on the other side. The two numbers team up to create a "match."

We have underlined our matches. There's a "2" on one side, and another "2" on the other side. This gives us our first match: 2. Our second match is also 2, since there is a second two on both sides. As shown in the picture below, the remaining numbers have no matches:

Now, list our matches. We have one match of "2" and another match of "2". We multiply our matches together:

The GCF = 4.

Divisibility Rules

An integer is divisible by:

2 if the integer ends in 0,2, 4, 6, 8.

5 if the integer ends in 0 or 5

10 if it ends in 0.

All even numbers end in 0,2,4,6,8,10 and are divisible by 2.

An integer is divisible by 3 if the sum

of its digits is divisible by 3.

An integer is divisible by 9 if the sum

of its digits is divisible by 9.

Example: 924 is divisible by 3

because

9+2+4 = 15.  15 is divisible by 3.

549 is divisible by 9 because 5+4+9 =

18.  18 is divisible by 9.