L3 · Prime or Composite (0 and 1 are neither)

Learning goal

“I can describe a number as prime or composite by counting its factors: a prime number has exactly two factors (1 and itself), a composite number has other factors too - and I know 0 and 1 are NEITHER prime nor composite.”

Prime number — a number with exactly two factors: 1 and itself. 7 is prime: its only factors are 1 and 7.

Composite number — a number with factors besides 1 and itself. 9 is composite: 1, 3, 9.

Neither — the label for 0 and 1. They are not prime and not composite; they get their own label.

Worked example

Is 11 prime or composite? List its factors (rainbow from L1): 1 x 11 works. 2? 11 / 2 leaves a remainder. 3? No. Nothing else divides 11 exactly before the pairs cross. Factors: 1, 11 - exactly TWO factors. A number with exactly two factors, 1 and itself, is prime. So 11 is prime. Now 15: factors 1, 3, 5, 15 - that is FOUR factors, more than two. Extra factors exist (3 and 5), so 15 is composite. Say it plainly: prime is not a feeling about a number - it is a count. Two factors: prime. More than two: composite.

Check yourself — explain it

9 is composite because...

Paired problem — example still visible

Is 13 prime or composite? -> Factors 1, 13 only -> Prime.

Faded completion — last step is yours

"17: 17 / 2, / 3, / 4 all leave remainders. Factors of 17: 1 and ___. So 17 is ___." -> 17; prime

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

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