4024/21 Oct/Nov 2025, Question 15: HCF with indices
Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 2 marks
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The question, in short
x = 2² × 3ⁿ⁺¹ × 7 and y = 2ⁿ × 3ⁿ × 7⁴, where n is an integer greater than 2. Find the HCF of x and y as a product of primes in terms of n.
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Solution · 2 marks
- 1Take the lower power of each common prime
- 22: lower of 2² and 2ⁿ (n > 2) is 2²; 3: lower of 3ⁿ⁺¹ and 3ⁿ is 3ⁿ; 7: lower of 7 and 7⁴ is 7
- 3HCF = 2² × 3ⁿ × 7
Answer2² × 3ⁿ × 7
Stuck on a step? Read the free lesson: HCF and LCM
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Also searched as: 4024/21/O/N/25 · 4024_w25_qp_21 · 4024 w25 21 · question 15.
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