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Prime Factorisation Exploration

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Prime Factorisation Exploration

The school radio team is preparing a number-themed quiz. Solve each challenge and show your reasoning where asked.

Warm up: spot the primes

Check what the radio team already knows about prime numbers.

1.The quiz producer needs one prime number for a sound-check code. Which number is prime?

2.A caller says 1 is prime because it has only one factor. Is the caller correct? Explain what makes a number prime.

3.For a quick quiz hint, complete the rule: A whole number greater than 1 is composite if it has more than positive factors.

Build the factor signals

Break each number into prime factors. A factor tree is one way to organise your thinking.

4.Anahera chooses 84 for the next radio quiz. Write its prime factorisation using indices where possible.

5.Tevita wants to show how 90 breaks down. Draw a factor tree for 90, ending with prime numbers.

Use this space for your factor tree for 90.

6.Charlotte checks a listener's answer: 120 = 2³ × 3 × 5. Is this a correct prime factorisation? Show a check by multiplying the factors.

7.Match each number to its prime factorisation for the quiz answer key.

3² × 5
2² × 3²
2³ × 7

Use prime factors to solve

The final radio round uses prime factorisation to compare and combine numbers.

8.Two station timers beep every 48 seconds and every 180 seconds. Use prime factorisation to find the greatest common factor of 48 and 180.

9.A broadcast effect repeats every 12 seconds, and a music cue repeats every 18 seconds. Use prime factors to find when they will happen together again.