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Euclid's division lemma, division algorithm and HCF sheet
5-mark answer frame

Use Euclid's division algorithm to find the HCF of three given numbers.

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 three numbers and 'To find: their HCF'.
  2. 2 · Write the formula or theorem. a = bq + r, 0 ≤ r < b, and HCF(a, b) = HCF(b, r).
  3. 3 · Find the HCF of two of the numbers. Divide the larger by the smaller, then the divisor by the remainder, until r = 0.
  4. 4 · Bring in the third number. Apply the algorithm to the third number and the HCF you just found.
  5. 5 · Verify the result. Divide each given number by your HCF; every division must be exact.
  6. 6 · Check and box the answer. Box the HCF, e.g. 'HCF = 198'.

Scoring tip: Write each division as a full line in the form a = bq + r. Examiners give step marks for every correct line.