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Fundamental theorem of arithmetic sheet
5-mark answer frame

Find the HCF and LCM of given numbers by prime factorisation.

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Write what is given and what is to be found. Write the numbers and 'To find: HCF and LCM'.
  2. 2 · Write the formula or theorem. Every composite number is a unique product of primes (fundamental theorem of arithmetic).
  3. 3 · Factorise each number. Use repeated division by primes. Write each number as powers of primes in ascending order.
  4. 4 · Find the HCF. Take the common primes with their smallest powers.
  5. 5 · Find the LCM. Take every prime with its greatest power.
  6. 6 · Check and box the answer. For two numbers, check HCF × LCM = product. For three, check that each number divides the LCM.

Scoring tip: Show the division ladder for each number. Writing the powers neatly, like 2³ × 3², earns the factorisation mark.