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**Q.1. ****Determine the H.C.F of the following numbers by using Euclid's algorithm (i-x):**

**(i) 300,450**

**(ii) 399,437**

**(iii) 1045,1520**

**Ans: **

**(i) **300 and 450

Dividend = 450 and divisor = 300

Clearly, the last divisor is 150.

Hence, HCF of the given numbers is 150.

**(ii) **399 and 437

We have dividend = 399 and divisor = 437

Clearly, the last divisor is 19.

Hence, HCF of the given numbers is 19.

**(iii) **1045 and 1520

We have dividend = 1045 and divisor = 1520

Clearly, the last divisor is 95.

Hence, HCF of the given numbers is 95.

**Q.2. ****Show that the following pairs are co-prime:**

**(i) 59,97**

**(ii) 875,1859**

**(iii) 288,1375**

**Ans: **We know that two numbers are co-primes if their HCF is 1.

**(i)** 59 and 97

Here, dividend = 97 and divisor = 59

Clearly, the last divisor is 1.

Hence, the given numbers are co-primes.

**(ii) **875 and 1859

Here, dividend = 1,859 and divisor = 875

Clearly, the last divisor is 1.

Hence, the given numbers are co-primes.

**(iii) **288 and 1375

Here, dividend = 288 and divisor = 1,375

Clearly, the last divisor is 1.

Hence, the given numbers are co-primes.

**Q.3. What is the H.C.F of two consecutive numbers?**

**Ans: **

The HCF of two consecutive numbers is 1.

Example:

D = 4 and d = 5 are two consecutive numbers.

Here, we have dividend = 5 and divisor = 4

Clearly, the last divisor is 1.

Hence, HCF of 4 and 5 is 1.

**Q.4. ****Write true (T) of false (F) for each of the following statements:**

**(i) The H.C.F of two distinct prime numbers is 1.**

**(ii) The H.C.F of two co-prime number is 1.**

**(iii) The H.C.F of an even and an odd numbers is 1.**

**(iv) The H.C.F of two consecutive even numbers is 2.**

**(v) The H.C.F of two consecutive odd numbers is 2.**

**Ans: **

**(i) **True.

**(ii) **True.

**(iii)** False.

HCF of 6 and 9 is 3, not 1.

**(iv) **True.

**(v) **False.

HCF of two consecutive odd number is 1.

Example: HCF of 25 and 27 is 1.

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