Prime Factorisation and HCF/LCM
Every composite number can be written as a unique product of prime factors. This prime factorisation allows us to find the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of two numbers systematically.
What You Need to Know
Key Concept Diagram
A prime number has exactly two factors: 1 and itself (e.g. 2, 3, 5, 7, 11, 13)
Every composite number can be expressed as a product of primes (Fundamental Theorem of Arithmetic)
A factor tree is a method for finding the prime factorisation of a number
HCF (Highest Common Factor): multiply shared prime factors at their lowest power
LCM (Lowest Common Multiple): multiply all prime factors at their highest power
Key Vocabulary
Prime Number
A whole number greater than 1 with exactly two factors: 1 and itself
Prime Factorisation
Expressing a number as a product of its prime factors, e.g. 60 = 2^2 x 3 x 5
HCF
Highest Common Factor: the largest number that divides exactly into two or more numbers
LCM
Lowest Common Multiple: the smallest number that is a multiple of two or more numbers
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is the prime factorisation of 36?
Question 2
What is the HCF of 24 and 36?
Question 3
What is the LCM of 4 and 6?
Key Concepts Summary
- ●A prime number has exactly two factors: 1 and itself (e.g. 2, 3, 5, 7, 11, 13)
- ●Every composite number can be expressed as a product of primes (Fundamental Theorem of Arithmetic)
- ●A factor tree is a method for finding the prime factorisation of a number
- ●HCF (Highest Common Factor): multiply shared prime factors at their lowest power
- ●LCM (Lowest Common Multiple): multiply all prime factors at their highest power