L1 · Factors of a Number within 100

Learning goal

“I can find ALL the factors of a number within 100 by working in factor pairs, and I can prove a number is a factor by dividing: a factor divides with remainder 0.”

Factor — a whole number that divides another number exactly, with no remainder. 3 is a factor of 12 because 12 / 3 = 4.

Factor pair — two factors that multiply to make the number. 3 and 4 are a factor pair for 12.

Remainder — what is left over after dividing. If the remainder is 0, the sharing was exact.

Array — counters arranged in equal rows and columns. A 3-by-4 array shows 12 as 3 x 4.

Worked example

Find all the factors of 12. Step 1: Start with 1. Every number has the pair 1 x 12, so 1 and 12 are factors. Step 2: Try 2. 12 / 2 = 6 exactly, so 2 x 6 is a pair: 2 and 6 are factors. Step 3: Try 3. 12 / 3 = 4 exactly, so 3 x 4 is a pair: 3 and 4 are factors. Step 4: Try 4. 4 is already in the rainbow - the pairs have crossed over, so we stop. The factors of 12, in order: 1, 2, 3, 4, 6, 12. Picture the pairs as a rainbow: 1 arcs to 12, 2 arcs to 6, 3 arcs to 4. Every factor has a partner, and the partners multiply to 12.

Check yourself — explain it

We can stop trying new numbers when...

Paired problem — example still visible

Find all the factors of 18. -> Pairs: 1 x 18, 2 x 9, 3 x 6. Factors: 1, 2, 3, 6, 9, 18.

Faded completion — last step is yours

"Factors of 20: pairs are 1 x 20 and 2 x 10. The next pair is 4 x ___." -> 5, so the factors are 1, 2, 4, 5, 10, 20.

Ready to practise?

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

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