Factors, multiples, and primes (age 11+)
Use the concepts and vocabulary of prime numbers, factors, multiples, common factors, common multiples, highest common factor (HCF), lowest common multiple (LCM), and prime factorisation including product notation and the unique factorisation property
What a learner can do afterwards
- Express any integer as a product of its prime factors using index notation
- Find the HCF and LCM of two numbers using prime factorisation
- Apply the unique factorisation theorem to explain why every number has exactly one set of prime factors
1 · Read
Say you have 24 strawberries and 36 blueberries, and you want to arrange them into the biggest matching trays with none left over. You already know what prime numbers, factors, and multiples are. Now you'll break any whole number down into the primes that build it, and write that breakdown quickly using index notation.
Take 24 = 2³ × 3 and 36 = 2² × 3². For the HCF, multiply the primes they share, using the lower power each time: 2² × 3 = 12. For the LCM, multiply every prime that appears, using the higher power each time: 2³ × 3² = 72. So the HCF of 24 and 36 is 12, and the LCM is 72.
Every whole number greater than 1 has exactly one set of prime factors. Divide by 2 first or by 3 first, and you still land on the same primes in the end. That's why it's called unique factorisation.
Break a number into primes with index notation, then use those same primes to find the HCF (shared primes, lower power) and LCM (all primes, higher power).
2 · Watch
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Where it sits
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.