**NUMBER SYSTEM** in Maths

What is Number System in Maths? A number framework is characterized as an arrangement of composing for communicating numbers. It is the numerical documentation for speaking to quantities of a given set by utilizing digits or different images in a predictable way.

**Whole Numbers:** The set of whole numbers is denote by “W”.

where “W” = { 0, 1, 2, 3, 4, 5, 6, …….}

**Natural Numbers**: The numbers which are use in counting are known as Natural Numbers or Positive Integers. Their set is denote by N.

Thus, N = { 1, 2, 3, 4, 5, 6, …….}

**Set of Integers:** All counting numbers. Their negatives and “O”, when combined from the set of integer. This is denote by I.

Thus I = ( ………… -3, -2, -1, 0, 1, 2, 3, ………….)

**Even Numbers:** Those numbers which are exactly divisible by 2 are known as even numbers.

For example 2, 4, 6, 8, 10, …………

**Odd Numbers:** The numbers which are not exactly divisible by 2 known as Odd Numbers.

Ex: 1, 3, 5, 7, 9, ……….

**Prime Numbers: **A number is said to be a Prime Number if its factors are “1” and the number itself only.

Ex: 2, 3, 5, 7, ……..

There are 25 prime numbers below 100.

**Composite Numbers **: The numbers which are not Prime are call “Composite Numbers”.

For example 4, 6, 8, 9, 12, ……….

**Rational Numbers:** A number of the form a/b where a and b are integers prime to each other b ≠ 0 is called a Rational Numbers.

**Irrational Numbers**: The numbers whose exact value cannot be determine are call Irrational Numbers.

For example √3, √5, √7, ……etc.

**Real Numbers**: Both Rational and Irrational Numbers are collectively known as Real Numbers.

**Important results Number System in Maths**

### Test of Divisibility

- A number is divisible by 2, if its units digit is 0 or even.
- 2) A number is divisible by 3, if the sum of the digits can be divide by 3.
- 3) A number is divisible by 4, if the number compose of the last two digits can be divide by 4 or the last two digits are zeros.
- 4) A number is divisible by 5, if the last digit is either 0 or 5.
- 5) A number is divisible by 6, if it is divisible by both 2 and 3.
- 6) A number is divisible by 8, if the number compos of the last three digits can be divide by 8 or the last three digits are zeros.
- 7) A number is divisible by 9, if the sum of the digits can be divid by 9.
- 8) A number is divisible by 11, if the sum of the digits in the odd place so the number and the sum of the digits in the even places are equal or the difference of these two sums is divisible by 11.
- 9) A number is divisible by 12, if it is divisible by both 3 and 4.
- 10) A number is divisible by 25, if it ends in ’25’, ’75’, ’00’.