Unit 3
5 marks · Normal(a) Express 84 and 126 as products of their prime factors in index form.
(b) Find the HCF and LCM of 84 and 126.
(c) An event A and an event B are combined. Event A has 3 outcomes, event B has 4 outcomes. List the total number of possible combined outcomes.
Express 84 and 126 as products of their prime factors in index form.
Find the HCF and LCM of 84 and 126.
List the total number of possible combined outcomes.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 84 = 2^2 × 3 × 7; 126 = 2 × 3^2 × 7
(b) HCF = 42, LCM = 252 · must show HCF=42, LCM=252
(c) 12 · must show 12
Common mistakes: Incorrectly factorising numbers; Confusing HCF and LCM
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Factorises 84 correctly.
A1 (a) · 1 mark · Factorises 126 correctly.
M2 (b) · 1 mark · Applies correct method for HCF/LCM using prime factors.
A2 (b) · 1 mark · Correct HCF (42) and LCM (252).
B1 (c) · 1 mark · Gives total outcomes as 3×4=12.
Worked solution
(a) 84 = 2×42 = 2×2×21 = 2×2×3×7 = 2^2×3×7; 126=2×63=2×3×21=2×3×3×7=2×3^2×7.
(b) HCF: take lowest powers of common primes: 2^1 × 3^1 × 7^1 = 42. LCM: highest powers: 2^2 × 3^2 × 7^1 = 252.
(c) 3 outcomes from A × 4 from B = 12 possible combined outcomes.