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.
An integer and give three examples
An integer is any whole number (not a fraction) that can be positive, negative, or zero.
Questions this Types of number deck will help you answer
- › Determine if 64 is a cube number. Explain your reasoning.
Define an integer and give three examples.
An integer is any whole number (not a fraction) that can be positive, negative, or zero.
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.
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.
Determine if 64 is a cube number. Explain your reasoning.
Yes, 64 is a cube number. This is because 4 x 4 x 4 = 64. It is the result of cubing the integer 4.
What are triangular numbers? Provide the first 4 triangular numbers.
Triangular numbers are formed by the sum of consecutive natural numbers.
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 (
What is the reciprocal of 5/3? Explain how to find the reciprocal of any number.
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.
Find the Highest Common Factor (HCF) of 12 and 18.
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.
What is the Lowest Common Multiple (LCM) of 4 and 6?
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.
Express 24 as a product of its prime factors (prime factorization).
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.
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.
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.
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.
What are triangular numbers? Provide the first 4 triangular numbers.
Triangular numbers are formed by the sum of consecutive natural numbers.
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 (
Tips to avoid common mistakes in Types of number
- ● A prime number has only two factors: 1 and itself, so test odd numbers for divisibility by other primes to confirm.
- ● To prove a number isn't prime, give a *specific* factor that divides it evenly — in this case, 111 ÷ 3 = 37.
- ● Remember 'product' means multiplication, and in maximizing a product, consider multiplying two negative numbers.
- ● Memorize the first 15 square numbers and the first 10 cube numbers for quick recall during the exam.
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.
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.
Related Mathematics guides
Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.
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