Page 157 - Ganit Kaushal

4. The number of common prime factors of 75, 60 and 105 is

(a) 2 (b) 3 (c) 4 (d) 5
5. Which of the following pairs is not co-prime?
(a) 8, 10 (b) 11, 12 (c) 1, 3 (d) 31, 33
6. Which of the following pairs of numbers are co-prime? (NCERT)

(a) 15 and 37 (b) 30 and 415 (c) 81 and 18 (d) 27 and 72
7. Fill in the blanks.
(a) The only natural number which has exactly one factor is __________.
(b) The only prime number which is even is__________.

(c) The two perfect numbers are __________ and __________.
(d) The only prime triplet is __________.
(e) __________ is a factor of every number.
(f) The number of factors of a prime number is __________.

(g) Two numbers having only 1 as a common factor are called __________ numbers.
(h) If a number has __________ in the ones place, then it is divisible by 10.
(i) A number for which the sum of all its factors is equal to twice the number is called a __________
number.
(j) The numbers having more than two factors are called __________ numbers.
(k) 2 is the only __________ number, which is even.

(l) If the sum of the digits is a __________ of 3, then the number is divisible by 3.
(m) In co-prime art, the thread will finally pass through a gap of pegs that is equal to their
__________.
8. State whether the following statements are True (T) or False (F).
(a) Every multiple of a number is greater than or equal to the number.

(b) Every number is a multiple of itself.
(c) All numbers that are divisible by 4 may not be divisible by 8.
(d) Every natural number has a finite number of factors.
(e) There are infinitely many prime numbers.

(f) The sum of two prime numbers is always an even number.
(g) The sum of two prime numbers is always a prime number.
(h) The sum of two prime numbers can never be a prime number.
(i) No odd number can be written as the sum of two prime numbers.

(j) If two numbers are co-prime, then at least one of them must be prime.
(k) If a number is divisible by 18, it must also be divisible by both 3 and 6.
(l) If a number is divisible by both 2 and 4, it must be divisible by 8.
(m) If a number is divisible by both 3 and 6, it must be divisible by 18.

(n) If a number is divisible by two primes, it is also divisible by their product.
(o) Two primes are co-prime to each other.

Prime Time 155