Page 145 - Ganit Kaushal

Ex 7. Which of the given numbers are prime? 23, 51, 37, 26. (NCERT)

Sol.  1 × 23 = 23 and 1 × 37 = 37 \ 23 and 37 are prime.
 They do not have a factor other than 1 and the number itself.
51 = 3 × 17; 26 = 2 × 13.
\ 51 and 26 are composites, not prime.

Ex 8. Write three pairs of prime numbers less than 20 whose sum is a multiple of 5. (NCERT)
Sol. Three pairs of prime numbers less than 20 whose sum is a multiple of 5 are: (3, 17), (7, 13), (2, 3)
Can you think of some more pairs?
Ex 9. The numbers 13 and 31 are prime numbers. Both these numbers have the same digits 1 and 3. Find
such pairs of prime numbers up to 100. (NCERT)
Sol. Other pairs are: (17, 71), (37, 73), (79, 97)
Ex 10. Find seven consecutive composite numbers between 1 and 100. (NCERT)

Sol. Seven consecutive composite numbers between 1 and 100 are: 90, 91, 92, 93, 94, 95, and 96.
Ex 11. Write all the twin prime pairs between 1 and 100. (NCERT)
Sol. All the twin prime pairs between 1 and 100 are: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43),
(59, 61), (71, 73).
Ex 12. Identify whether each statement is true or false. Explain. (NCERT)
(a) There is no prime number whose units digit is 4.

(b) A product of primes can also be prime.
(c) Prime numbers do not have any factors.
(d) All even numbers are composite numbers.
(e) 2 is prime, and so is the next number, 3. For every other prime, the next number is composite.
Sol. (a) True [ It will have a divisor 2]

(b) False [ It will have a divisor other than 1 and itself]
(c) False [ 1 and the number itself are always the factors]
(d) False [ 2 is an even and prime number]
(e) True

Exercise 5.2

1. Which of the following numbers is the product of exactly three distinct prime numbers:
45, 60, 91, 105, 330? (NCERT)
2. How many three-digit prime numbers can you make using each of 2, 4 and 5 once? (NCERT)
3. Observe that 3 is a prime number, and 2 × 3 + 1 = 7 is also a prime. Are there other primes for which
doubling and adding 1 gives another prime? Find at least five such examples. (NCERT)
4. Look at the list of primes till 100. What is the smallest difference between two successive primes?
What is the largest difference? (NCERT)
5. Are there an equal number of primes occurring in every row in the Sieve of Eratosthenes? Which
decades have the least number of primes? Which has the maximum number of primes? (NCERT)

6. We see that 2 is both a prime and an even number. Is there any other even prime? (NCERT)

Prime Time 143