Types of number Cambridge IGCSE Mathematics revision
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In plain words
Numbers come in families. Some can only be divided by 1 and themselves: the primes. Every other whole number can be broken down into primes multiplied together, like a wall into bricks. Once you can do that, common factors and multiples are easy.
Three things to know
- A factor divides into a number exactly. A multiple is in its times table. A prime number has exactly two factors, 1 and itself (so 1 is not prime).
- Any whole number can be written as a product of prime factors: 60 = 2² × 3 × 5.
- HCF: the largest number that divides into both. LCM: the smallest number that both divide into. Rational numbers can be written as fractions; irrational numbers, such as π and √2, cannot.
Worked example
Find the HCF and LCM of 12 and 18.
- Write each as a product of primes: 12 = 2² × 3 and 18 = 2 × 3².
- HCF: take the lowest power of each prime they share: 2 × 3 = 6.
- LCM: take the highest power of every prime: 2² × 3² = 36.
Tips and tricks
- 1 is not a prime number, and 2 is the only even prime.
- A check: HCF × LCM equals the two numbers multiplied together. 6 × 36 = 216 = 12 × 18.
It lands in your notebook with its questions as flashcards.
Types of number: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
Which of these is a prime number?
21, 27 and 33 all divide by 3.
What is the highest common factor of 18 and 30?
6 is the largest number that divides into both.
What is the lowest common multiple of 6 and 10?
30 is the first number in both times tables.
Which number is irrational?
7 is not a square number, so its root cannot be written as a fraction.
What is the value of 2³ × 5?
8 × 5.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
4 questions, 8 marks. Write your answers on paper, then check them.
Types of number
Cambridge IGCSE Mathematics 0580 · 8 marks · papermunch.org
Name ______________________________ Date ______________
Write 84 as a product of its prime factors.[2]
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2² × 3 × 7.
Find the highest common factor of 24 and 60.[2]
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12. (24 = 2³ × 3 and 60 = 2² × 3 × 5; shared: 2² × 3.)
Find the lowest common multiple of 8 and 12.[2]
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24.
Which of these are irrational: √9, π, 0.25, √5?[2]
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π and √5. (√9 = 3 and 0.25 = 1/4 are rational.)
Answers: Types of number
- 1. 2² × 3 × 7.
- 2. 12. (24 = 2³ × 3 and 60 = 2² × 3 × 5; shared: 2² × 3.)
- 3. 24.
- 4. π and √5. (√9 = 3 and 0.25 = 1/4 are rational.)