NATURAL NUMBERS

Natural numbers – We know , we use 1, 2, 3, 4,……when we begin to count. They come naturally when we start counting . Hence, mathematicians call the counting numbers as natural numbers.

How to add natural numbers

To add a natural number of any digit write the number below one another. We can write the number in any order. Place the numbers , in such a way that the ones place is matching.Then add till the number of places.

Look at the picture below to add a natural number.

How to subtract natural numbers

To subtract a natural number of 1 digit , 2 digit , 3 digit or any digit write the biggest number first then the smallest number. Write the number below one another .Place the numbers , in such a way that the ones place is matching. Now subtract till the number of places.

*FACTORS*

**WHAT IS FACTOR**

If we divide a number with any number and if we get the reminder 0 that number is the factor of the first number.

**HOW TO FIND A FACTOR OF A NUMBER**

To find a factor of a number we should divide the number with 1 . Then we should divide that number with 2 and if the remainder is 0 , that number is the factor of 2. Continue this process till the half of the number.

**WHAT IS PRIME NUMBER**

Prime number are numbers that have 2 factors. Those factors are 1 and the number itself.

**WHAT IS PRIME FACTOR**

The factors of a number with the prime number is called the prime factors of the number.

**WHAT IS PRIME FACTORIZATION ? HOW TO FIND OUT ?
**

The method using to find the prime factors of a number is called prime factorization of the prime factors of a number .

There are two methods to do prime factorization . They are 1 . Factor tree 2. Prime factorization

** FACTOR TREE **

**PRIME FACTORIZATION **

**HOW TO FIND FACTORS OF A NUMBER USING PRIME FACTORS**

To find all factors of a number multiply all possible combination.

Now look at the examples shown below.

**LCM – LOWEST COMMON MULTIPLE**

Method 1 – In this method, first we have to write the numbers as shown in the fig. . Now we can select any smallest number which should be at least divisible with any one of the number. Now we can divide each number with the divisor. If the number is divisible with divisor, then we can write the quotient bellow that number. If the number is not divisible then we can directly bring down the number itself. Now repeat the process as shown in the figure until all the numbers reach 1. Then by multiply all the divisors we will get the LCM.

**HCF – HIGHEST COMMON FACTOR
**

Method 1 – In this method first write the numbers as shown in the given fig.Now we should write the least possible number which should be divisible with all the numbers. Repeat this process till there is no more possible number that should be divisible with all the number.Then multiply all the divisor to get the HCF. If there is only one divisor , that divisor is the HCF of all the number.

**CO – PRIME NUMBER**

Two numbers that have 1 as the only common factor is known as co – prime numbers.

TWIN PRIME NUMBERS

Two consecutive prime numbers with only 1 composite number is called twin prime numbers

Example : 11 , 13

PRIME TRIPLE

Three consecutive prime numbers with only 1 composite prime number is called prime triple.

Example : 3, 5, 7

# Divisibility rule of numbers 1 to 11

###### Divisibility rule of numbers 1

Number 1 is divisible with all numbers.

###### Divisibility rule of numbers 2

If a number is an even number then it is divisible by 2. Or if the last digit (ones place) of the number is 0,2,4,6,8, then it is divisible by 2.

Example : 24 , 32 , 50 .

###### Divisibility rule of numbers 3

The given number is divisible by 3, then the sum of the all digits if the number will be the multiple of 3.

Example : 54 = 5 + 4 =9

###### Divisibility rule of numbers 4

A number with 3 or more digits is divisible with 4, then the number formed by it last 2 digits (once and tens place) will be divisible with 4.

Example : 524

###### Divisibility rule of numbers 5

The number which has either 0 or 5 in its once place is divisible with 5.

Example : 235 , 350

###### Divisibility rule of numbers 6

If a number is divisible with 2 and 3 both then the number is divisible with 6 also.

Example : 24 Last digit is 4 . It is divisible by 2. 2+4 = 6 . 6 is divisible with 3. therefore , 24 is divisible by 6

###### Divisibility rule of numbers 8

A number with 4 or more digit is divisible by 8, if the number formed by its last 3 digit is divisible by 8.

Example : 3248

###### Divisibility rule of numbers 9

If the sum of the digits of a number is divisible by 9 then the number itself is divisible by 9.

Example : 99 = 9+9=18

###### Some more divisibility rules

- If a number is divisible by another number, then it is divisible by each of the factors of that number.

Ex : 24 is divisible by 8 . It is divisible by each of the factors of 8. Factors of 8 are 1 , 2 , 4 and 8. So 1,2,4 and 8 are also the factors of 24.

- If a number is divisible by two co-prime numbers, then it is divisible by it product also.

Ex :The number 80 is divisible by 4 and 5 . It is also divisible by 4 multiplied by 5 = 20 . 4 and 5 are co – prime numbers.

- If two given number are divisible by a number, then their sum is also divisible by that number.

Ex : The numbers 16 and 20 are both divisible by 4 . The number 16 +20 = 36 is also divisible by 4.

- If two given number are divisible by a number, then their difference is also divisible by that number.

Ex : The numbers 35 and 20 are both divisible by 5 . There difference is 35 – 20 = 15 . It is divisible by 5.

*BASIC GEOMETRICAL IDEAS*

**Point**

Point is the basic unit of geometry. it have no length breadth and no thickness. That means point have no dimensions. It can be represented by dot and can be called as dotA.

**LINE **

a line is a collection of points going endlessly in both directions along a straight path.

**Plane**

A plane is a smooth flat surface which extends endlessly in all directions. It does not have boundaries. A plane have only length and breadth but no thickness.

**Line segment**

A line segment is the part of the line with 2 endpoints. It can also define as the shortest distance between 2 points. (line segment PQ).

**Ray**

Ray is the part of the line with one start point and extended endlessly in one direction.

**Angle**

**Interior of an angle**

The space with in the arms of an angle is called interior of the angle.

**Exterior of an angle**

The space outside the arms of an angle is called exterior of an angle.

**Adjacent angles**

Two angles which have a common arm,a common vertex, and the non common arm lie on either side of common arm are called adjacent angles.

**curves**

a curve is a collection of points going endlessly in both directions along a straight or curved path.

**Simple curve**

Any curve which does not cross itself and can be draw without taking the pencil is called simple curve.

**Open curve**

Any curve which have a start point and an end point then it is called open curve.

**Closed curve**

Any curve which have no start point and no end point then it is called closed curve.

**Different spaces in a closed curve**

- Interior of the curve (inside )
- Boundary (on the curve)
- Exterior of the curve (outside)

The interior and boundary together in a closed curve is called the region

**Polygons**

The simple closed curve made up with line segment is called polygon

**Side, Vertex, Diagonals of a polygon**

The line segments used to form a polygon is called **side. **

The common points of two sides (line segments) in a polygon is called **vertex**.

The line segment between two opposite vertex of a polygon is called **diagonal** of the polygon.

**Adjacent vertex**

If two vertex of a polygon formed by at least one common side is called adjacent vertex.

**Opposite vertex**

If two vertex of a polygon formed by no common side is called opposite vertex.