GCSE Maths · Higher · Chapter 1: Basic number · Lesson 2

Primes, factors, LCM and HCF

Grades 4–7About 50 minutesNo calculator37 marks

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NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

Grades 4–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

Write $360$ as a product of its prime factors. Give your answer in index form.

Hint Divide by the smallest prime that goes in, again and again, until you reach 1.

B1
Write $588$ as a product of its prime factors. Give your answer in index form.
[2 marks]
Answer

Example 2

Find the highest common factor (HCF) and the lowest common multiple (LCM) of $140$ and $196$ .

Hint For the HCF take the shared primes at the lower power. For the LCM take every prime at the higher power.

B2
Find the highest common factor (HCF) and the lowest common multiple (LCM) of $96$ and $150$ .
[3 marks]
AnswerHCF $= \dots\dots$ LCM $= \dots\dots$

Grades 5–6

C1
$A = 2^{3} \times 5^{2} \times 7$ and $B = 2^{2} \times 5 \times 7^{2}$ . Work out the HCF of $A$ and $B$ . Give it as an ordinary number.
[2 marks]
Answer
C2
$1200 = 2^{a} \times 3 \times 5^{b}$ . Find the value of $a$ and the value of $b$ .
[2 marks]
Answer $a = \dots\dots$ $b = \dots\dots$

C3
Work out $(- 2)^{3} - 4 \times (- 3)$ .
[2 marks]
Answer
C4
Find the smallest whole number $k$ such that $90 k$ is a square number.
[2 marks]
Answer
C5
The Venn diagram shows the prime factors of two numbers, $A$ and $B$ . Work out the HCF and the LCM of $A$ and $B$ .
[2 marks]
AnswerHCF $= \dots\dots$ LCM $= \dots\dots$
C6
Work out $2^{4} \times 3^{2} \times 5^{2}$ . Give your answer as an ordinary number.
[2 marks]
Answer
C7
Between which two consecutive whole numbers does $3100$ lie?
[1 mark]
Answer $\dots\dots$ and $\dots\dots$
C8
Show that $91$ is not a prime number.
[1 mark]

Grades 6–7

D1
Ali runs one lap of a track in $84$ seconds. Ben runs one lap in $105$ seconds. They start together from the same point and keep running. After how many minutes are they next at the start together? You must show your working.
[3 marks]
Answer

D2
A gardener has $120$ tulip bulbs and $168$ daffodil bulbs. She plants all of them in rows. Every row has the same number of tulips and the same number of daffodils. She wants as many rows as possible.
(a)
Write $120$ and $168$ as products of their prime factors.
[2 marks]
(b)
Work out the greatest number of rows she can plant.
[2 marks]
Answer
(c)
How many bulbs are in each row?
[1 mark]
Answer
Total for D2: 5 marks
D3
Sam says, "The LCM of $36$ and $54$ is $1944$ , because $36 \times 54 = 1944$ ."
Explain why Sam is wrong. Work out the LCM of $36$ and $54$ .
[3 marks]
Answer

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can write a number as a product of its prime factors in index form.
I can use prime factors to find the HCF and LCM of two numbers.
I can work out expressions with negative numbers and powers.

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