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**1.** Find the H CF of 231 and 396, using Euclid’s division algorithm.

**2.** Can two numbers have 18 as their HCF and 380 as their LCM? Give reason.

**3.** Show that the square of an odd positive integer is of the form 8m + 1, for some wholenumber m.

**Hint: **

For a whole number ‘q’, we have (2q + 1) any positive integer.

∵ (2q + 1)^{2} = 4q^{2} + 4q + 1 = 4q(q + 1) + 1

Since, q(q + 1) is either 0 or even

∵ Let it be 2m, where m is a whole number

⇒ (2q + 1)^{2} = 4[q(q + 1)] + 1

= 4[2m] + 1

= 8m + 1

**4.** Find the largest number which divides 248 and 1032 leaving remainder 8 in each case.

**5.** Given that LCM of two numbers is 1449 and their HCF is 23. If one of the numbers is 207, find the other.

**6.** Find the greatest number of 6-digits which is exactly divisible by 15, 24 and 36.

**7.** Prove tha teach of the following is an irrational.

**8.** Prove that p is not a rational number, if p is not a perfect square.

**9. **Prove that the difference and quotient of are irrational.

**ANSWERS**

1. 33

2. No, [∵ the HCF (18) does not divide LCM (380)]

4. 16

5. 161

6. 999720

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