L1 · Factors and building products in many ways

Learning goal

“I can find all the factor pairs of a number using arrays and a factor rainbow, and I can build the same product in different ways by regrouping.”

Product — the result of multiplying. In 3 × 4 = 12, the product is 12.

Factor — a number that is multiplied. In 3 × 4 = 12, the factors are 3 and 4.

Factor pair — two factors that multiply to give a product, like 3 and 4 for 12.

Array — dots or tiles arranged in equal rows and columns, like 3 rows of 4.

Worked example

Find all the factor pairs of 12. Build each pair as an array: 1 row of 12, 2 rows of 6, 3 rows of 4. Turning an array on its side gives the same pair (4 rows of 3 is the pair 3 and 4 again), so stop when the pairs start repeating. Rainbow: write the pairs as arcs — 1–12, 2–6, 3–4. The rainbow is complete. The factor pairs of 12 are (1, 12), (2, 6), (3, 4).

Check yourself — explain it

Why isn't 5 a factor of 12?

Paired problem — example still visible

Find all the factor pairs of 16. → (1, 16), (2, 8), (4, 4)

Faded completion — last step is yours

“Factor pairs of 20: 1 × 20, 2 × 10, and ___ × ___.” → 4 × 5, so the pairs are (1, 20), (2, 10), (4, 5)

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

Start practice →Take the unit quiz