Guided Practice

Exercise 1.1 - Euclid’s Division Algorithm

Apply the chapter concepts in short, focused steps. Use hints when you need a nudge and open the worked solution once you have attempted the problem.

Exercise 1 of 1 2 questions 2 hints

Practice Snapshot 2 solutions

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Exercise 1.1

Questions

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Hints

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Worked Solutions

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2 questions ready for practice in this set

Question 1

Use Euclid’s division algorithm to find the HCF of 135 and 225.

Hint Apply division repeatedly until remainder becomes zero.

Worked solution

<pre>
225 = 135 × 1 + 90
135 = 90 × 1 + 45
90 = 45 × 2 + 0

HCF = 45
</pre>

Question 2

Find the HCF of 196 and 382 using Euclid’s division algorithm.

Hint Divide larger number by smaller repeatedly.

Worked solution

<pre>
382 = 196 × 1 + 186
196 = 186 × 1 + 10
186 = 10 × 18 + 6
10 = 6 × 1 + 4
6 = 4 × 1 + 2
4 = 2 × 2 + 0

HCF = 2
</pre>