- Books Name
- CBSE Class 6 Mathematics Book

- Publication
- Param Publication

- Course
- CBSE Class 6

- Subject
- Mathmatics

**Factors**

Any number which is an exact divisor of a given number is called a factor of the given number.

For example factor of 6 are 1,2,3 and 6

Important results :

(a) 1 is a factor of every number.

(b) Every number is a factor of itself.

(c) Every factor of a number is always equal to or less than the number.

(d) Every number has a finite number of factors.

- Books Name
- Class 6 Mathematics Book

- Publication
- ReginaTagebücher

- Course
- CBSE Class 6

- Subject
- Mathmatics

**CHAPTER - 03**

**PLAYING WITH NUMBERS**

**Prime and Composite Numbers**

A Prime number is a number which has exactly two factors i.e. ‘1’ and the number itself. A composite number has more than two factors, which means piecemeal from getting divided by 1 and the number itself, it can also be divided by at least one positive integer. 1 isn't a prime or composite number. Except these two numbers, there's also same order of numbers which are co prime numbers.

** Detailed explanations of these numbers are given below.**

**Prime Numbers**

** Illustration of Prime Number**

3 is a prime number because 3 can be divided by only two numbers

i.e. 1 and 3 itself.

3/1 = 3

3/3 = 1

in the same way, 2, 5, 7, 11, 13, 17 are prime numbers.

**Composite Numbers**

A composite number has more than two factors, which means aside from getting divided by the number 1 and itself, it can also be divided by at least one integer or number. We don't consider ‘1’ as a composite number.

**Illustration of Composite Number**

12 is a composite number because it can be divided by 1, 2, 3, 4, 6 and 12. So, the number ‘12’ has 6 factors.

•12/1 = 12

•12/2 = 6

•12/3 = 4

•12/4 = 3

•12/6 = 2

•12/12 = 1

**Types of composite Numbers**

There are two types of composite Numbers

1. Even composite Numbers

2. Odd composite Numbers

**Odd Composite Numbers**

The odd positive integers or the odd Numbers that aren't prime Numbers are called odd composite Numbers. For illustration, 9, 21, 33, 45, etc., are odd composite Numbers.

**Even Composite Numbers**

The even Numbers that aren't prime Numbers are called even composite Numbers. For illustration, 4, 10, 16, 28, 56, etc., are even composite Numbers.

**Sieve of Eratosthenes **is a system to find the prime Numbers and composite Numbers from the group of Numbers. A Greek Mathematician Eratosthenes, in the third century B.C introduced this.

The Sieve of Eratosthenes system is easy to find the prime Numbers from a set of Numbers.

**The way to find the prime Numbers**

from 1 to 100 are as follows

**Step 1** First write all the natural Numbers from 1 to 100,row-wise and column-wise as shown in the below figure.

**Step 2** put a cross over 1, as it's neither a prime number nor a composite.

**Step 3 **Now, encircle the number 2(which is a prime number) and cross all the multiples of 2, similar as, and so on. Since all the multiples of 2 are composite.

**Step 4** next, encircle the number 3, and put a cross over all the multiples of 3, similar as, etc. Since piecemeal from 3 all its multiples are composite.

**Step 5** makes circle the number 5 and put a cross over all the multiples of 5.

**Step 6 **Now encircle 7 and cross all the multiples of 7

**Step 7** Encircle 11 and cross all the multiples of 11

**Step 8 **Continue the process unless all the Numbers are moreover encircled or crossed.

**Composite number **is a number with any set of Numbers that don't have any other common factor other than 1. It's also known as fairly prime Numbers.

**Properties of co-prime Numbers**

• All prime Numbers are co-prime to each other.

• Any successive whole Numbers are always co-primed.

• Sum of any two co-prime Numbers is always co-primed.

•Co-prime Numbers need not be prime Numbers.

**Twin prime **are a match of prime numbers that differ by 2.

**3.1 Factors and Multiples**

The numbers that can be divided completely by another number is known as factor.

When a number is multiplied by a natural number then the number we get in result is called Multiple of that Number.

**E.g.** 18 is a multiple of 1,2,3,6,9,18 and

∴ 2,5 and 10 are the factors of 10.