Factors: integers or expressions that divide something exactly 15 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.

List the Factors 12 3b3

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

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

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

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

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

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