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Prime Numbers Exploration

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Prime Numbers Exploration

Aotearoa’s Coastal Rescue team is packing emergency kits. Use prime numbers and factor pairs to check the kit counts. Show your reasoning where asked.

Prime-number checks

Remember: a prime number has exactly two positive factors, 1 and itself. One is neither prime nor composite.

1.The team has 29 signal flares. Is 29 prime or composite? Give a factor pair check to support your answer.
2.Which number in the supply list is composite? Select the correct answer: 37, 39, 41 or 43.
  • 37
  • 39
  • 41
  • 43
3.Classify each number as prime, composite, or neither: 1, 2, 27, 31.

Factor-pair investigations

A factor pair multiplies to make the target number. Finding all factor pairs reveals whether a number has more than two factors.

4.A rescue station has 36 water bottles. List every positive factor pair of 36, then state how many factors 36 has.
5.The team needs to split 45 first-aid packs into equal-sized groups with none left over. Write all possible group-size factor pairs for 45.
6.Rangi says, “Every odd number is prime.” Use an odd composite number to show why this claim is incorrect, and explain.

Prime factorisation

Break a composite number into prime factors. Keep splitting until every factor is prime.

7.Factor 60 completely into prime factors. Write the prime factorisation as a multiplication statement and in index form.
8.A store cupboard contains 84 torches. Find the prime factorisation of 84, showing a valid sequence of factor splits.
9.Find the prime factorisation of 49. Show the factor split that proves all factors are prime.
10.Challenge: Find the prime factorisation of 30. Show a sequence of factor splits until every factor is prime.

3 printable pages

  • Prime Numbers Exploration, page 1 of 3: Prime-number checks, Factor-pair investigations

    Page 1

  • Prime Numbers Exploration, page 2 of 3: Prime factorisation

    Page 2

  • Prime Numbers Exploration, page 3 of 3: 10. Challenge: Find the prime factorisation of 30. Show a sequence of factor splits until…

    Page 3

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