State whether the following statements are true (T) or false (F):

(i) Every natural number has a finite number of factors.

(ii) Every natural number has an infinite number of its multiples.

(iii) There are infinitely many prime numbers.

(iv) The HCF of two numbers is smaller than the smaller of the numbers.

(v) The LCM of two numbers is greater than the larger of the numbers.

State whether the following statements are true or false. If a statement is false, justify your answer:

(i) The sum of two prime numbers is always an even number.

(ii) The sum of two prime numbers is always a prime number.

(iii) The sum of two prime numbers can never be a prime number.

(iv) No odd number can be written as the sum of two prime numbers.

(v) If two numbers are co-prime, then atleast one of them must be prime.

(vi) If a number is divisible by 18, it must be divisible by 3 and 6 both.

(vii) If a number is divisible by 2 and 4 both, it must be divisible by 8.

(viii) If a number is divisible by 3 and 6 both, it must be divisible by 18.

(ix) HCF of an even number and an odd number is always 1.

Which of the following is an odd composite number?

1. 7

2. 9

3. 11

4. 12

The number of even numbers between 68 and 90 is

1. 10

2. 11

3. 12

4. 31