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Cambridge IGCSE Maths (0580) · Topic 1: Number · 1.1

Cambridge IGCSE Maths 0580 Types of Number Questions

Types of Number questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.

Practise types of number →Types of Number notes

What the syllabus asks

Summarised in our own words: check the exact wording in the official 0580 syllabus.

Types of Number questions: Core

For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).

Question 1 Core non-calculator · easy

Here is a list of numbers: \(3, \ 8, \ 12, \ 19, \ 27, \ 33, \ 49, \ 51\)
From the list, write down
(a) the prime numbers
(b) the cube numbers
(c) the numbers that are factors of \(24\).

Show the worked answer
  1. (a) \(33 = 3 \times 11\), \(49 = 7 \times 7\), \(51 = 3 \times 17\), \(27 = 3 \times 9\), and \(8\) and \(12\) are even. Only \(3\) and \(19\) have exactly two factors.
  2. (b) \(8 = 2^3\) and \(27 = 3^3\).
  3. (c) \(24 \div 3 = 8\), \(24 \div 8 = 3\) and \(24 \div 12 = 2\); no other number in the list divides \(24\) exactly.

Answer: (a) \(3, 19\) (b) \(8, 27\) (c) \(3, 8, 12\)

Question 2 Core non-calculator · easy

Write down the reciprocal of
(a) \(0.2\)
(b) \(2\frac{1}{2}\)

Show the worked answer
  1. (a) \(0.2 = \frac{1}{5}\), so its reciprocal is \(\frac{5}{1} = 5\).
  2. (b) \(2\frac{1}{2} = \frac{5}{2}\), so its reciprocal is \(\frac{2}{5}\).

Answer: (a) \(5\) (b) \(\frac{2}{5}\)

Question 3 Core non-calculator · easy · 2 marks

Write down the reciprocal of

(a) \(5\) (b) \(\frac{2}{3}\)

Show the answer and mark scheme
  • B1 (a) 1/5
  • B1 (b) 3/2 oe

Answer: (a) \(\frac{1}{5}\) (b) \(\frac{3}{2}\)

Question 4 Core non-calculator · medium

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

Show the worked answer
  1. Divide by primes: \(360 \div 2 = 180\), \(180 \div 2 = 90\), \(90 \div 2 = 45\), \(45 \div 3 = 15\), \(15 \div 3 = 5\), and \(5\) is prime.
  2. So \(360 = 2 \times 2 \times 2 \times 3 \times 3 \times 5\).
  3. In index form: \(2^3 \times 3^2 \times 5\).

Answer: \(2^3 \times 3^2 \times 5\)

Question 5 Core non-calculator · medium

Find (a) the highest common factor (HCF) and (b) the lowest common multiple (LCM) of \(84\) and \(120\).

Show the worked answer
  1. \(84 = 2^2 \times 3 \times 7\) and \(120 = 2^3 \times 3 \times 5\).
  2. (a) HCF: the lower power of each shared prime, \(2^2 \times 3 = 12\).
  3. (b) LCM: the higher power of every prime, \(2^3 \times 3 \times 5 \times 7 = 840\).

Answer: (a) \(12\) (b) \(840\)

Question 6 Core non-calculator · medium

Here are six numbers: \(\sqrt{16}, \ \sqrt{20}, \ \pi, \ 0.\dot{3}, \ \frac{22}{7}, \ \sqrt[3]{27}\)
Write down the irrational numbers.

Show the worked answer
  1. \(\sqrt{16} = 4\), \(\sqrt[3]{27} = 3\), \(0.\dot{3} = \frac{1}{3}\) and \(\frac{22}{7}\) can all be written as a fraction, so they are rational.
  2. \(20\) is not a square number, so \(\sqrt{20}\) cannot be written as a fraction; \(\pi\) is irrational (\(\frac{22}{7}\) is only an approximation to it).

Answer: \(\sqrt{20}\) and \(\pi\)

Question 7 Core non-calculator · medium

Two numbers are written as products of primes: \(P = 2^4 \times 3 \times 7\) and \(Q = 2^2 \times 3^3 \times 5\).
Work out (a) their highest common factor (b) their lowest common multiple, as ordinary numbers.

Show the worked answer
  1. (a) Shared primes with the lower powers: \(2^2 \times 3 = 12\).
  2. (b) Every prime with the higher power: \(2^4 \times 3^3 \times 5 \times 7 = 16 \times 27 \times 35 = 15\,120\).

Answer: (a) \(12\) (b) \(15\,120\)

Question 8 Core calculator · medium · 2 marks

Find the lowest common multiple (LCM) of 18 and 30.

Show the answer and mark scheme
  • M1 lists multiples or writes 18 = 2 × 3² and 30 = 2 × 3 × 5
  • A1 90

Answer: \(90\)

Question 9 Core calculator · medium · 2 marks

Here are five numbers: \(\sqrt{16}, \quad \sqrt{7}, \quad 0.333\ldots \text{ (recurring)}, \quad \pi, \quad \frac{5}{9}\)

Which of them are irrational?

Show the answer and mark scheme
  • B2 √7 and π only (B1 for one of them and no wrong number)

Answer: \(\sqrt{7}\) and \(\pi\)

Question 10 Core non-calculator · hard

A red light flashes every \(18\) seconds and a green light flashes every \(30\) seconds. They flash together at the start.
How many more times do they flash together in the next \(10\) minutes?

Show the worked answer
  1. They flash together every LCM of \(18\) and \(30\) seconds. \(18 = 2 \times 3^2\), \(30 = 2 \times 3 \times 5\), so the LCM is \(2 \times 3^2 \times 5 = 90\) seconds.
  2. \(10\) minutes \(= 600\) seconds, and \(600 \div 90 = 6.66\ldots\)
  3. So they flash together \(6\) more times (at \(90, 180, \ldots, 540\) seconds).

Answer: \(6\) times

Examiner Insights: common mistakes in IGCSE Maths 0580, with fixes (our analysis of public sources) →

Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).

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Questions students ask

Which Cambridge 0580 papers can test types of number?

Types of Number is on both tiers (syllabus 1.1), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.

Are these Cambridge past-paper questions?

No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.

Where can I practise more types of number questions?

In the 0580 practice for topic 1 (Number), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.

More number questions