1.1

Types of number

Cambridge IGCSE Mathematics (0580)  · Unit 1: Number  · 10 flashcards

Types of number is topic 1.1 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 1 — Number , alongside Fractions, decimals and percentages, Operations and order of operations and Powers and roots.  In one line: An integer is any whole number (not a fraction) that can be positive, negative, or zero.

This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.

The deck below contains 10 flashcards — 5 definitions and 1 key concept — covering the precise wording mark schemes reward.  Use the 5 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.

Key definition

An integer and give three examples

An integer is any whole number (not a fraction) that can be positive, negative, or zero.

Example: -3, 0, 7.

Questions this Types of number deck will help you answer

Definition Flip

Define an integer and give three examples.

Answer Flip

An integer is any whole number (not a fraction) that can be positive, negative, or zero.

Example: -3, 0, 7.
Definition Flip

What is a prime number? Give an example of a prime number between 20 and 30.

Answer Flip

A prime number is a whole number greater than 1 that has only two factors: 1 and itself.

Example: 23 (only divisible by 1 and 23).
Definition Flip

What is a square number? Give an example of the first 5 square numbers.

Answer Flip

A square number is the result of multiplying an integer by itself.

Example: 1 (1x1), 4 (2x2), 9 (3x3), 16 (4x4), 25 (5x5).
Key Concept Flip

Determine if 64 is a cube number. Explain your reasoning.

Answer Flip

Yes, 64 is a cube number. This is because 4 x 4 x 4 = 64. It is the result of cubing the integer 4.

Definition Flip

What are triangular numbers? Provide the first 4 triangular numbers.

Answer Flip

Triangular numbers are formed by the sum of consecutive natural numbers.

Example: 1, 3 (1+2), 6 (1+2+3), 10 (1+2+3+4).
Definition Flip

Explain the difference between rational and irrational numbers. Provide an example of each.

Answer Flip

A rational number can be expressed as a fraction p/q, where p and q are integers and q ≠ 0 (

Example: 0.5, -2/3). An irrational number cannot be expressed as a fraction (. π, √2).
Key Concept Flip

What is the reciprocal of 5/3? Explain how to find the reciprocal of any number.

Answer Flip

The reciprocal of 5/3 is 3/5. To find the reciprocal, invert the fraction (swap the numerator and denominator). For a whole number, place it over 1 first, then invert.

Key Concept Flip

Find the Highest Common Factor (HCF) of 12 and 18.

Answer Flip

The HCF of 12 and 18 is 6. Factors of 12 are: 1, 2, 3, 4, 6, 12 and factors of 18 are: 1, 2, 3, 6, 9, 18. The highest number present in both is 6.

Key Concept Flip

What is the Lowest Common Multiple (LCM) of 4 and 6?

Answer Flip

The LCM of 4 and 6 is 12. Multiples of 4 are: 4, 8, 12, 16,... and multiples of 6 are: 6, 12, 18,... The lowest number present in both lists is 12.

Key Concept Flip

Express 24 as a product of its prime factors (prime factorization).

Answer Flip

24 = 2 x 2 x 2 x 3, or 2³ x 3. We find this by successively dividing by prime numbers until we reach 1.

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1.2 Fractions, decimals and percentages

Key Questions: Types of number

Define an integer and give three examples.

An integer is any whole number (not a fraction) that can be positive, negative, or zero.

Example: -3, 0, 7.
What is a prime number? Give an example of a prime number between 20 and 30.

A prime number is a whole number greater than 1 that has only two factors: 1 and itself.

Example: 23 (only divisible by 1 and 23).
What is a square number? Give an example of the first 5 square numbers.

A square number is the result of multiplying an integer by itself.

Example: 1 (1x1), 4 (2x2), 9 (3x3), 16 (4x4), 25 (5x5).
What are triangular numbers? Provide the first 4 triangular numbers.

Triangular numbers are formed by the sum of consecutive natural numbers.

Example: 1, 3 (1+2), 6 (1+2+3), 10 (1+2+3+4).
Explain the difference between rational and irrational numbers. Provide an example of each.

A rational number can be expressed as a fraction p/q, where p and q are integers and q ≠ 0 (

Example: 0.5, -2/3). An irrational number cannot be expressed as a fraction (. π, √2).

Tips to avoid common mistakes in Types of number

More topics in Unit 1 — Number

Types of number sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.

Cambridge syllabus keywords to use in your answers

These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.

integer positive negative prime square number cube number triangular number rational irrational real number reciprocal common factor common multiple HCF LCM prime factor prime factorisation natural number whole number

Key terms covered in this Types of number deck

Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.

An integer and give three examples
Prime number? Give an example of a prime number between 20 and 30
Square number? Give an example of the first 5 square numbers
Triangular numbers? Provide the first 4 triangular numbers
Explain the difference between rational and irrational numbers. Provide an example of each

Related Mathematics guides

Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.

How to study this Types of number deck

Start in Study Mode, attempt each card before flipping, then rate Hard, Okay or Easy. Cards you rate Hard come back within a day; cards you rate Easy push out to weeks. Your progress is saved in your browser, so come back daily for 5–10 minute reviews until every card reads Mastered.