What knowledge do students gain from Exercise 5.2 in Chapter 5?

The exercise helps demonstrate how to simplify numbers into their prime factors using factor trees and division.

Why is prime factorisation significant in maths?

Prime factorisation is relied upon for finding HCF, LCM, and simplifying very large numbers.

What types of questions are asked in this exercise?

The exercise provides questions to find, and write the prime factors of some given numbers.

Do these solutions assist students in maths olympiads?

It develops your number skills and allows you to deal with factor based olympiad questions at a much faster pace.

What skills would students develop by doing this practice exercise?

Students will develop logical thinking, step-by-step problem solving skills, and knowledge of number properties.

NCERT Class 6 Maths Ch 5 Exercise 5.2 Solutions

NCERT Solutions Class 6 Maths Chapter 5 Prime Time Exercise 5.2

Exercise 5.2 in the NCERT 8 Maths Chapter 5 Prime Time, helps to familiarize you with the concept of prime factorisation and learn how to break down numbers into their prime factors using simple methods like factor trees.

These solutions have been developed according to the latest syllabus from the CBSE and NCERT. The questions in this exercise guide you through the steps to finding the prime factors of given numbers.

These NCERT Solutions are written in simple language and consist of clear steps in logic to help learn the solutions without confusion. The solutions can also assist you with preparing for your examinations and save time for revision. You can print or download the free PDF for continued practice at any time.

3.0NCERT Class 6 Maths Chapter 5 Prime Time Exercise 5.2: Detailed Solutions

How many prime numbers are there from 21 to 30 ? How many composite numbers are there from 21 to 30 ? Sol. Prime numbers are numbers that have only two divisors: 1 and the number itself. The prime numbers between 21 and 30 are: 23 and 29. So, there are 2 prime numbers. Composite numbers are numbers that have more than two divisors. The composite numbers between 21 and 30 are:

21, 22, 24, 25, 26, 27, 28, 30

. So, there are 8 composite numbers.

We see that 2 is a prime and also an even number. Is there any other even prime? Sol. No, 2 is the only even prime number. Since 2 is the only even number that meets the criteria of a prime number (its only divisors are 1 and 2), it is the only even prime number. All other even numbers are divisible by 2 and at least one other number, so they are not prime.

Look at the list of primes till 100 . What is the smallest difference between two successive primes? What is the largest difference? Sol. To find the smallest difference between two successive prime numbers up to 100, let's list the prime numbers in that range and calculate the differences between each pair: Prime numbers up to

100 : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73

, 79, 83, 89, 97. Differences between successive primes:

$3 - 2 = 1$	$43 - 41 = 2$
$5 - 3 = 2$	$47 - 43 = 4$
$7 - 5 = 2$	$53 - 47 = 6$
$11 - 7 = 4$	$59 - 53 = 6$
$13 - 11 = 2$	$61 - 59 = 2$
$17 - 13 = 4$	$67 - 61 = 6$
$19 - 17 = 2$	$71 - 67 = 4$
$23 - 19 = 4$	$73 - 71 = 2$
$29 - 23 = 6$	$79 - 73 = 6$
$31 - 29 = 2$	$83 - 79 = 4$
$37 - 31 = 6$	$89 - 83 = 6$
$41 - 37 = 4$	$97 - 89 = 8$

The smallest difference between two successive primes up to 100 is 1 (between the primes 2 and 3). The largest difference between two successive primes up to 100 is 8 , which occurs between the primes 89 and 97.

Are there an equal number of primes occurring in every row in the table on the previous page? Which decades have the least number of primes? Which have the most number of primes?

Sol. There is not an equal number of primes in every row. The number of primes varies between rows. The decade 91-100 has the least number of primes with only 1 prime (97). The decades 1-10 and 11-20 have the greatest number of primes, each with 4 primes.

Which of the following numbers are prime?

23, 51, 37, 26

Sol. The prime numbers from the list

(23, 51, 37, 26)

are 23 and 37 . 23: Prime (it has no divisors other than 1 and 23). 51: Not prime (it is divisible by 1,3 and 17). 37: Prime (it has no divisors other than 1 and 37). 26: Not prime (it is divisible by 1,2 and 13 ).

Write three pairs of prime numbers less than 20 whose sum is a multiple of 5 . Sol. Three pairs of prime numbers less than 20 whose sum is a multiple of 5 are:

(2, 3), (2, 13)

and

(7, 13)

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. Sol. The valid pairs of prime numbers up to 100 that consist of the same digits are:

(13, 31), (17, 71), (37, 73)

and

(79, 97)

Find seven consecutive composite numbers between 1 and 100 . Sol. The seven consecutive composite numbers are:

90, 91, 92, 93, 94, 95, 96

Twin primes are pairs of primes having a difference of 2 . For example, 3 and 5 are twin primes. So are 17 and 19. Find the other twin primes between 1 and 100. Sol. Twin primes between 1 and 100: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61) and

(71, 73)

Identify whether each statement is true or false. Explain. (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 a prime and so is the next number, 3 . For every other prime, the next number is composite. Sol. (a) True A prime number must end in

1, 3, 7

, or 9 (except for the number 2 ) because any number ending in

0, 2, 4, 6

or 8 is divisible by 2 . Thus, there is no prime number whose unit digit is 4 . (b) False A product of prime numbers is only prime if it involves exactly one prime number. When you multiply two or more prime numbers together, the result is always a composite number, not a prime. As this number has more than 2 factors now. (c) False Prime numbers have exactly two factors 1 and itself. (d) False The number 2 is an even number, but it is not composite. As it is a prime number. (e) True For every prime number greater than 2 , the next number is composite.

Which of the following numbers is the product of exactly three distinct prime numbers: 45 ,

60, 91, 105, 330

? Sol. Here,

45 = 3 \times 3 \times 5

( 2 distinct primes)

60 = 2 \times 2 \times 3 \times 5

( 3 distinct primes)

91 = 7 \times 13

( 2 distinct primes)

105 = 3 \times 5 \times 7

( 3 distinct primes)

330 = 2 \times 3 \times 5 \times 11

(4 distinct primes) Number 105 is the product of exactly three distinct prime numbers i.e.

3 \times 5 \times 7

How many three-digit prime numbers can you make using each of 2,4 , and 5 once? Sol. 2, 4 and 5 cannot form a single prime number. Because, when its units digit is 2 or 4 it is divided by 2 , and when units digits is 5 it is divided by 5 so that's why 2 , 4 and 5 cannot form a prime number.

Observe that 3 is a prime number, and

2 \times 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. Sol. The five prime numbers for which doubling and adding 1 gives another prime are: 2 (since

2 \times 2 + 1 = 5

) 3 (since

2 \times 3 + 1 = 7

) 5 (since

2 \times 5 + 1 = 11

) 11 (since

2 \times 11 + 1 = 23

) 23 (since

2 \times 23 + 1 = 47

)

4.0Key Features and benefits for Class 6 Maths Chapter 5 Exercise 5.2

This activity describes how to find prime factors of numbers by using necessary techniques.

It contains questions which will adequately prepare students for topics like HCF and LCM.

Regular practice of NCERT Solutions helps in solving quick problems for school and class assessments.

The NCERT Solutions will also help you prepare for maths olympiad questions that require instant number recognition and analysis.

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