Page 155 - Ganit Kaushal

Miscellaneous Solved Examples

There are four options (Q. 1 to Q. 6), out of which only one is correct. Choose the correct option.
Ex 1. All prime factors of 6 are

(a) 1, 6 (b) 2, 3 (c) 1, 2, 3 (d) 1, 2, 3, 6
Sol. (b)  Factors of 6 = 1, 2, 3, and 6. \ Prime factors of 6 = 2, 3.
Ex 2. All factors of 6 are
(a) 1, 6 (b) 2, 3 (c) 1, 2, 3 (d) 1, 2, 3, 6

Sol. (d) Factors of 6 = 1, 2, 3, 6.
Ex 3. Every natural number has an infinite number of
(a) prime factors (b) factors (c) multiples (d) none of these
Sol. (c) Any number multiplied by a natural number gives a multiple, and since there are infinite natural
numbers, a number has infinite multiples.

Ex 4. Which of the following numbers is divisible by 4?
(a) 308594 (b) 506784 (c) 732114 (d) 9301538
Sol. (b) A number is divisible by 4 if the number formed by its last two digits is divisible by 4. In 506784,
the last two digits form (84), which is divisible by 4.
Ex 5. Which of the following numbers is divisible by 8?
(a) 503786 (b) 505268 (c) 305678 (d) 703568

Sol. (d) Since the number formed by the last three digits of 703568 is (568), which is divisible by 8.
Ex 6. Which of the following numbers is divisible by 3?
(a) 50762 (b) 42063 (c) 52871 (d) 37036
Sol. (b) Since the sum of the digits of 42063 is 4 + 2 + 0 + 6 + 3 = 15, which is divisible by 3.

Ex 7. Fill in the blanks.
(a) The smallest even number is __________.
(b) Every non-prime number is called a __________ number.
(c) __________ and __________ are neither prime nor composite numbers.
(d) The smallest odd composite number is __________.

(e) All prime numbers, except 2, are __________.
Sol. (a) 2 (b) composite (c) 0 and 1 (d) 9
(e) odd numbers
Ex 8. State whether the following statements are True (T) or False (F).

(a) The sum of two prime numbers is always even.
(b) 2 is the only even prime number.
(c) All even numbers are composite numbers.
(d) The product of two even numbers is always even.

(e) Two prime numbers are always co-prime numbers.
(f) The sum of two co-prime numbers is always co-prime with their product.

Prime Time 153