Prime factorisation for HCF
To find the HCF by prime factorisation, write both numbers as products of primes and take only the common prime factors with the smallest powers.
Practice This ConceptMain explanation
Teacher explanation
The HCF must divide both numbers fully, so it can only use the prime factors that are common to both numbers. For each common prime, we choose the smaller power, because the smaller count is the limit shared by both numbers.
Example
36 = 2^2 x 3^2 and 48 = 2^4 x 3, so the HCF is 2^2 x 3 = 12.
Simple analogy
For HCF, keep the common primes and trim the powers.
Common confusion
Students often take the largest powers of common primes, which gives the LCM idea instead of the HCF.
Exam tip
For HCF, remember the phrase: common primes with minimum powers.
Answer writing and exam use
1-mark use
Write the exact meaning of prime factorisation for hcf in one clean line.
2-mark use
Define prime factorisation for hcf and add one example or condition.
3-mark use
Explain prime factorisation for hcf, show the method or example, and mention the common mistake.
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