1. Factors: integers or expressions that divide something exactly15
ab2
So if 15 is the product, what integers divide it exactly? We can divide it by 1, 3,5 and 15. To find these numbers we can also think about the numbers that multiply together to make it. These are the factors because we can split it into these parts without a remainder, without a decimal or fraction answer. Thinking about ab^2, what can we divide it by so that we don’t get a fraction? If we divided by 3, we would have no choice but to write the answer ab^2/3, it can’t be simplified. But if we divide this expression by a, the a’s would cancel each other out and we get b^2. So a divides this expression exactly. So does b, So does ab and b^2.

2. List the Factors 12
3b3

3. List the Factors
4ab2
2b3
What factors do they have in common?

4. Highest common factor 25 30 ab 2a2 & &
The biggest number that will divide both numbers, or expressions.
&

5. Highest common factor 2a 10b 3b 4a & &
The biggest number that will divide both numbers, or expressions.
&

6. Highest common factor 6ab3 2b2 4x3 12xy & &
The biggest number that will divide both numbers, or expressions.
&

7. 12, 18, 30
ab2, 2ab
4a2b2 , 2b3
3ab, 9a3
8xy5, 2x2y
6) 9y2, 2x2
7) 2g2 , 4ag, 6ag3
8) 3ab3, 15b, 2b2
9) 8ab3, 2a2, 6ab
10) 15, 3a2, 18ab

8. 12, 18, 30 = 6
ab2, 2ab = ab
4a2b2 , 2b3 = 2b2
3ab, 9a3 = 3a
8xy5, 2x2y = 2xy
6) 9y2, 2x2 = 1
7) 2g2 , 4ag, 6ag3 = 2g
8) 3ab3, 15b, 2b2 = b
9) 8ab3, 2a2, 6ab = 2a
10) 15, 3a2, 18ab = 3