Real numbers - Exercise 1.1

Exercise 1.1 1. Use Euclid’s division algorithm to find the HCF of (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255 2. Show that any positive odd integer is of form 6q +1, or 6q +5, where q is some integer. 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? 4. Use Euclid’s division lemma to show that the square of any positive integer is either of form 3m or 3m + 1 for some integer m. 5. (Hint: Let x be any positive integer then it is of the form 3q, 3q+1 or 3q+2). Now square each of these and show that they can be rewritten in the form 3m or 3m+1).