CHAPTER 1 : Real Numbers

Exercise 1.1

1. Use Euclid’s division algorithm to find the HCF of :
1. 135 and 225
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2. 196 and 38220
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3. 867 and 255
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2. Show that any positive odd integer is of the form 6𝓆 + 1, or 6𝓆 + 3, or 6𝓆 + 5, where 6𝓆 is some integer.
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3. An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?
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4. Use Euclid's division lemma to show that the square of any positive integer is either of the form 3𝓂 or 3𝓂 + 1 for some integer 𝓂.
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5. Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9𝓂, 9𝓂 + 1 or 9𝓂 + 8.
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