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. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Is 1 prime, composite, or neither?
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Neither. 1 has only one factor (itself), so it fails both definitions.
2 List the prime numbers between 10 and 20. (list them separated by commas)
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11, 13, 17, 19. 15 divides by 3 and 5; the rest are even.
3 Is 138 divisible by 3?
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1 + 3 + 8 = 12, a multiple of 3 → yes.
Level 2 · Core
4 Write 36 as a product of primes using indices. (as a simplified expression)
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36 = 4 × 9 = 2 × 2 × 3 × 3 = 22 × 32.
5 Write 100 as a product of primes using indices. (as a simplified expression)
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100 = 4 × 25 = 2 × 2 × 5 × 5 = 22 × 52.
6 Is 91 prime?
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No — 91 = 7 × 13. It is a classic "looks prime but is not".
Level 3 · Challenge
7 Find the HCF of 48 and 72.
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Lowest powers: 23 × 3 = 24.
8 Find the LCM of 12 and 18.
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Highest powers: 22 × 32 = 36.
9 Two alarms sound every 9 and 15 minutes, starting together. After how many minutes do they next sound together?
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9 = 32, 15 = 3 × 5 → LCM = 32 × 5 = 45 minutes.