06_CBSE_PRIME NUMBERS, TWIN PRIME NUMBERS & CO-PRIME NUMBERS

06_CBSE_PRIME NUMBERS, TWIN PRIME NUMBERS & CO-PRIME NUMBERS

Introduction

Prime numbers, twin prime numbers, and co-prime numbers are fundamental concepts in number theory that have numerous applications in mathematics and other fields. In this section, we will explore the definitions, properties, and examples of these concepts.

Prime Numbers

A prime number is a positive integer that is divisible only by itself and 1.

Properties of Prime Numbers:

1. Prime numbers have exactly two distinct factors: 1 and the number itself.

2. Prime numbers are greater than 1.

3. Prime numbers play a crucial role in number theory and cryptography.

Example:

The first few prime numbers are 2, 3, 5, 7, 11, and 13.

Twin Prime Numbers

Twin prime numbers are pairs of prime numbers that differ by 2.

Properties of Twin Prime Numbers:

1. Twin prime numbers are pairs of prime numbers.

2. The difference between twin prime numbers is always 2.

Example:

Some examples of twin prime numbers are (3, 5), (5, 7), (11, 13), and (17, 19).

Co-Prime Numbers

Co-prime numbers, also known as relatively prime numbers, are pairs of numbers that have no common factors other than 1.

Properties of Co-Prime Numbers:

1. Co-prime numbers have a greatest common divisor (GCD) of 1.

2. Co-prime numbers are not necessarily prime numbers themselves.

Example:

Some examples of co-prime numbers are (8, 15), (17, 23), and (25, 32).

Prime numbers, twin prime numbers, and co-prime numbers are essential concepts in number theory that have numerous applications in mathematics and other fields. Understanding these concepts is crucial for problem-solving and critical thinking in mathematics.

 

Practice Paper

MATHEMATICS

Class-06

Prime numbers, Twin prime numbers & Co-prime numbers

 

Section A

1. Which of the following numbers is a prime number?                                                    1

(a) 4                                 (b) 6                                 (c) 7                                 (d) 8

2. Which is the even prime number                                                                                   1

(a) 2                                 (b) 8                                 (c) 6                                 (d) 7

3. Which of the following pairs of numbers are twin prime numbers?                             1

(a) (3, 5)                          (b) (5, 7)                          (c) (11, 13)                      (d) All of the above

4. What is the difference between twin prime numbers?                                                  1

(a) 1                                 (b) 2                                 (c) 0                                 (d) Not fixed

 

Section B

5. List the first five prime numbers.                                                                                   2

6. Find a pair of co-prime numbers.                                                                                   2

7. Identify the prime numbers from the following list: 2, 4, 6, 7, 9, 11.                            2

8. Find a pair of co-prime numbers between 20 and 30.                                                    2

9. Find all the twin prime numbers less than 20.                                                                2

10. Find the prime factorization of 24 and 124                                                                    3

11. Determine if the numbers 14 and 25 are co-prime.                                                        3

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