Year 7 - Number

The Factor Apothecary

Begin with the simplest factor test: even numbers always split into two equal groups. From that one move, build factor pairs, common factors, and the highest common factor.

10fixed whiteboard questions
50random drill questions
3sections
Section I: even numbers and the divide-by-2 move.
Section II: factor pairs from clean divisions.
Section III: common factors and highest common factor.
Pedagogy: the first 10 questions are identical for every student so they can be modelled on the whiteboard.
Teaching path

Start With Even Factors

1. An even number has factor 2

If a number ends in 0, 2, 4, 6, or 8, it is even. That means it can be split into two equal groups, so 2 is a factor.

28/ 214

So 28 has the factor pair 2 x 14.

2. Keep dividing while it stays even

The first division by 2 is often not the end. If the new number is also even, divide by 2 again.

48/224/212/26/23

This shows 48 = 2 x 2 x 2 x 2 x 3. The repeated twos are useful because many common factors are built from them.

3. Factor pairs come from clean splits

A factor pair is two whole numbers that multiply to the target number.

36 = 2 x 18 36 = 3 x 12 36 = 4 x 9 36 = 6 x 6

Every clean split gives another way to see the number.

4. Common factors are shared splits

For two even numbers, 2 is immediately a common factor. Then compare what remains.

36/218 60/230
18/29 30/215
9/33 15/35
The shared factors were 2, 2, and 3. Multiply them: 2 x 2 x 3 = 12. So the HCF of 36 and 60 is 12.

The repeatable method

  1. Check whether both numbers are even.
  2. If they are, divide both by 2 and keep the shared 2.
  3. Repeat while both new numbers are even.
  4. Then test small odd factors such as 3, 5, 7, and 11.
  5. Multiply all the shared factors you collected.
Next: 10 fixed whiteboard questions
Journal

Factor Journal