Prime Numbers and Factors
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Prime Numbers and Factors
📚 Part 1: Multiple Choice
✏️ Part 2: Short Answers — HCF and LCM
🔑 Answer Key
Answer: 29 (only has factors 1 and 29)
Answer: 59 (only has factors 1 and 59)
Answer: 2 and 17 (2 is the only even prime number; 17 only has factors 1 and 17; 9 = 3 × 3)
Answer: 91 (91 = 7 × 13)
Answer: 41, 43, 47, 53, 59
Answer: HCF = 12
Working: 48 = 2⁴ × 3, 84 = 2² × 3 × 7. HCF = 2² × 3 = 12
Answer: HCF = 9
Working: 63 = 3² × 7, 81 = 3⁴. HCF = 3² = 9
Answer: LCM = 24
Working: 6 = 2 × 3, 8 = 2³. LCM = 2³ × 3 = 24
Answer: LCM = 35 (since 7 and 5 are both prime and have no common factors)
Answer: To find the HCF using prime factorisation, multiply together all the common prime factors using the lowest power that appears in both numbers.
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