# Number System quantitative aptitude concept and formula

Number system is an important part of quantitative aptitude part of all exams like ibps po clerk ssc and other exams.It can contain questions related to sum, multiplication, division and remainder related problems.Let us learn basic concept of number system.

## Number system for ibps clerk po and other exams

Let’s consider a number 45,312 .
Face value of 1 is 1.
Place or Local value of 1 is 1$\times {10}$ = 10
Face value of a digit is the value of digit itself.

### Types Of Numbers:-

1.Natural number : Counting numbers 1,2,3,4…… are called natural numbers.
2.Whole Numbers : All counting numbers together with zero are called whole numbers.
0,1,2,3,4,5…………
Note- Zero is the only whole number which is not a natural number.
3.Integers : All natural numbers, 0, and negative of counting numbers together form the set of integers.
{…….-3, -2, -1, 0, 1, 2, 3….}
4.Even number : The number divisible by 2 is even number.
Ex-2,4,6,8…
5.Odd number : The number not divisible by 2 is called odd number.
Ex-1,3,5,7….
6.Prime number : A number greate than 1 and has exactly two factors 1 and itself is called prime number.
Ex- 2, 3, 5, 7, 11…

#### Intext question on number system

To test whether 191 is prime or not-
Solution-Let’s find out a whole number just greater than square root of 191.
The number is 14.
Prime number less than 14 are 2,3,5,7,11,13
191 is not divisible by any of them.
So,191 is prime number.

7.Composite Number-Note- 1 is neither a prime nor a composite number.
2 is the only even prime number which is composite.
There are 25 prime numbers between 1 and 100.

### Types of divisibilty:-

1.Divisible by 2 –A number is divisible by 2 if it’s unit digit is any of 0,2,4,6,8
Ex-112456 is divisible by 2.

2.Divisibility by 3 –A number is divisible by 3 if the sum of digits is divisible by 3
Ex-135 is divisible by 3 because 1+3+5=9 which is divisible by 3

3.Divisible by 4 – A number is divisible by 4 if its last two digit is divisible by 4
Ex- 11524 is divisible by 4 because last two digit 24 is divisible by 4.

4.Divisible by 5 – A number is divisible by 5 if it’s unit digit is either 0 or 5.
Ex-222565 is divisible by 5 because its unit digit is 5.

5.Divisible by 6 – A number is divisible by if it is divisible by 2 and 3.

6.Divisible by 8- A number is divisible by 8 if it’s last 3 digit is divisible by 8.
Ex-125648 is divisible by 8 because 648 is divisible by 8.

7.Divisible by 9- A number is divisible by 9 if the sum of digit is divisible by 9.
Ex-60732 is divisible by 9.
6+0+7+3+2=18 is divisible by 9.

8.Divisible by 10- A number is divisible by 10 if its unit digit is 0.
Ex-1250 is divisible by 10.

9.Divisible by 11 – A number is divisible by 11 , if the difference of the sum of it’s digits at odd places and the sum of it’s digits at even places is either 0 or a number divisible by 11.
Ex- 4832718
The sum at odd place = (8+7+3+4)-(1+2+8)=11 which is divisible by 11.

### Basic formula of number system:-

• $(a+b)^{2}=a^{2}+b^{2}+2ab$
• $(a-b)^{2}=a^{2}+b^{2}-2ab$
• $(a+b)^{2} - (a-b)^{2}=4ab$
• $(a+b)^{2} + (a-b)^{2}=2(a^{2}+b^{2})$
• $(a)^{2} - (b)^{2}=(a+b)(a-b)$
• $(a+b+c)^2=(a)^{2} + (b)^{2} + (c)^{2}+2(ab+bc+ac)$
• $(a^3+b^3)=(a+b)(a^2-ab+b^2)$
• $(a^3-b^3)=(a-b)(a^2+ab+b^2)$
• If a+b+c=0 then $a^3+b^3+c^3=3abc$

Multiplication trick:-
45699 * 9999 = 45699 * (10000-1) = 456990000 – 45699 = 4569441301
Try to break one factor into sum or difference of numbers having more zeroes.

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