Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown.
Level 1 · Warm-up
1 Write 12 as a product of primes. (write the primes out in full, smallest first)
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12 = 3 × 4, and 4 = 2 × 2, so 12 = 2 × 2 × 3.
2 Write 20 as a product of primes. (write the primes out in full, smallest first)
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20 = 4 × 5, and 4 = 2 × 2, so 20 = 2 × 2 × 5.
3 A factor tree ends with the leaves 2, 3 and 5. What number was at the top?
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2 × 3 × 5 = 30.
Level 2 · Core
4 Write 36 as a product of primes, using indices. (as a product of prime powers, smallest prime first)
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36 = 4 × 9 = 2 × 2 × 3 × 3 = 22 × 32.
5 Write 40 as a product of primes, using indices. (as a product of prime powers, smallest prime first)
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40 = 8 × 5 = 2 × 2 × 2 × 5 = 23 × 5. The 5 appears once, so it needs no index.
6 A number has the prime factorisation 2 × 32. What is the number?
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32 = 9, and 2 × 9 = 18.
Level 3 · Challenge
7 Write 84 as a product of primes, using indices. (as a product of prime powers, smallest prime first)
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84 ÷ 2 = 42, 42 ÷ 2 = 21, and 21 = 3 × 7, so 84 = 22 × 3 × 7.
8 Kai splits 72 as 6 × 12 and Mia splits it as 8 × 9. Once both trees are finished, whose prime factorisation is correct? Answer Kai, Mia, or both.
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Both. Kai ends with 2, 3, 2, 2, 3 and Mia ends with 2, 2, 2, 3, 3 — the same primes, so both give 23 × 32.
9 Write 126 as a product of primes, using indices. (as a product of prime powers, smallest prime first)
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126 ÷ 2 = 63, and 63 = 9 × 7 = 3 × 3 × 7, so 126 = 2 × 32 × 7.