# CHAPTER 1 : Real Numbers

## Exercise 1.1

- Use Euclid’s division algorithm to find the HCF of :
- 135 and 225
answer
- 196 and 38220
answer
- 867 and 255
answer

- Show that any positive odd integer is of the form 6𝓆 + 1, or 6𝓆 + 3, or 6𝓆 + 5, where 6𝓆 is
some integer.
answer
- 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?
answer
- 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.
answer
- Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9𝓂, 9𝓂 + 1 or
9𝓂 + 8.
answers