A factor shares a number into equal rows. Make every rectangle of dots you can, then find factors and multiples.
How many rows?
Put the 8 dots into equal rows. Which numbers of rows make a rectangle?
A factor shares a number into equal rows: 3 is a factor of 12.
Factors come in pairs: 3 rows of 4 is 3 × 4.
Dots left over mean it isn't a factor.
Multiples are the times table: 4, 8, 12, 16…
A factor goes into a number exactly: 3 is a factor of 12. A multiple is in a number's times table: 12 is a multiple of 3. So factors are smaller (or the same), and multiples are bigger (or the same).
Try to put that many dots into equal rows: 1 row, 2 rows, 3 rows and so on. Every number of rows that leaves nothing over is a factor, and the length of the row is its partner. Once the pairs start to repeat, turned round, you have them all.
Two numbers that multiply to make the number. The factor pairs of 12 are 1 × 12, 2 × 6 and 3 × 4. Each pair is a rectangle of 12 dots: its rows and its columns.
Children skip count in multiples from about 6 to 8, use the word multiple at about 8 to 9, and find factors and factor pairs at about 9 to 10, once they know their times tables.