Worksheets · Foundation and Higher

Primes, factor trees, HCF and LCM

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Non-calculator · 4 marks
Answer each part without a calculator.
(a) Write down all the factors of $18$ . (1)
(b) Write down the prime numbers in this list: $21$ , $23$ , $25$ , $27$ , $29$ . (1)
(c) Write $60$ as a product of its prime factors. (2)
Question 2Non-calculator · 3 marks
(a) Two lights flash together. One then flashes every 18 seconds and the other every 24 seconds. How many seconds pass before they next flash together? (3)
Question 3Non-calculator · 6 marks
$A = 2^3 \times 3^2 \times 5$ and $B = 2^2 \times 3^4 \times 7$
(a) Find the highest common factor of $A$ and $B$ . (2)
(b) Find the lowest common multiple of $A$ and $B$ . You may leave your answer as a product of powers of prime factors. (2)
(c) $k$ is the smallest whole number such that $A \times k$ is a square number. Find $k$ . (2)

Answers and marks

(a) $1, 2, 3, 6, 9, 18$

(b) $23$ and $29$

(c) $2^2 \times 3 \times 5$

M1 A correct first split, such as $2 \times 30$ or $6 \times 10$ , continued at least once.
A1 $2 \times 2 \times 3 \times 5$ or $2^2 \times 3 \times 5$ .

(a) $72$ seconds

(a) $36$ $(2^2 \times 3^2)$

(b) $2^3 \times 3^4 \times 5 \times 7 = 22\,680$

(c) $10$

P1 Recognising that each prime power must become even, and naming $2$ and $5$ as the primes to multiply by.
A1 The correct answer, $10$ .

Primes, factor trees, HCF and LCM

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