# Quantitative Aptitude – Understand Number System easily?

This chapter of Number System, simplification, and approximation is the most important chapter in whole Quantitative aptitude. This chapter forms the basis of many other topics in Quantitative math. You are advised to go through this chapter with the utmost care.

## Number System in Quantitative Aptitude

Let us begin Number System by understanding various types of numbers.

## Natural Numbers

The numbers which are used for counting and is denoted by N. Natural numbers can never be negative or zero.“1 is the smallest natural number”

Example: Natural numbers are 1,2,3,4,5,6,7,8,…..

Is 0 a natural numbers?

No, 0 is not considered as a natural number. In fact it is considered as whole number.

Natural numbers are further classified :

• Even Numbers: The Numbers which are divisible by 2 are known as even numbers. For example: 2,4,6,8,10…”2 is the smallest even number
• Odd Numbers: The Numbers which are not divisible by 2 are known as odd numbers. For example:1,3,5,7,9…“1 is the smallest odd number”
• Prime Numbers: The numbers which are not divisible by any other number except 1 and itself are known as prime numbers. For example:2,3,5,7,11…
• Co-prime Numbers: Two numbers can be said to be co-prime if their highest common factor is ‘1″. For example:(4,5),(13,29) etc.
• Composite Numbers: Numbers Which are divisible by others numbers along with 1 and itself are known as composite numbers: For example: 4,6,8,10,12,14
Why 1 is not considered as prime and composite number?
Prime numbers should be divisible by 1 and itself . It means we should be two divisor. In this case we have only one divisor that is 1 itself. So 1 is not considered as prime number.
Composite numbers  also need two divisors. In this case we have only one divisor that is 1 itself. So 1 is not considered as composite number.

## Whole Numbers

All the natural numbers along with 0 are known as whole numbers. For example:0,1,2,3,4,5,6,7,8…” 0 is the smallest whole number”

## Integers

All counting numbers including 0 are known as integers. They are further classified into:

• Positive Integers: All integers which are positive are known as positive integers. For example:1,2,3,4,5,6…
• Negative Integers: All integers which are negative are known as negative integers. For example:-1,-2,-3,-4,-5…

The numbers which are either rational or irrational are known as real numbers.For example: 38,0,-5,1/3,π all are real numbers. They are further classified into two types.

## Real Numbers

• Rational Numbers: Any numbers which can be expressed in the form of p/q where p and q both are integers and q≠0. For example:3/5,-3/5 etc.
• Irrational Numbers: The numbers which cannot be expressed in the form of p/q where p and q both are integers and q≠0 are known as irrational numbers. For example: 3,5,π etc.

## Imaginary Numbers

Those numbers which are non real are known as imaginary numbers. For example: -5,-3,-7. Imaginary numbers are denoted by ‘iota'(i).

Here we will attend a short quiz of Quantitative Aptitude which will help us to understand what we have studied.

[ays_quiz id=’2′]

## Division(Quantitative Aptitude)

Let us consider A and B are two numbers then A/B is known as Division where A is the dividend and B is the divisor. Quotient, the result obtained by dividing one number by another.

Dividend =Divisor X Quotient

## Rules(numbers 2-8)

• A number is divisible by 2 if the digit at unit’s place is even or zero. For example:24,486,1286 etc
• A number is divisible by 3 if the sum of all digits are divisible by 3. For example:381(3+8+1=12, 12/3=4) This number is divisible by 3.
• A number is divisible by 4 if the number formed by last two digits is divisible by 4. For example:14084(in this number 84 is completely divisible by 4 ), hence 14084 is completely divisible by 4
• A number is divisible by 5 if the digit at unit’s place is 5 or zero. For example:12500( the digit at unit’s place is 0), hence this number is completely divisible by 5.
• A number is divisible by 6 if the number is divisible by both 2 and 3. For example:1320(the number is completely divisible by 2 and 3), hence this number is completely divisible by 6.
• A number is divisible by 7 if the difference between twice the digit at unit’s place and the remaining digits is either 0 or multiple of 7.Foe example:294(4*2=8, 29-8=21 and 21 is divisible by 7), hence this number is completely divisible by 7.
• A number is divisible by 8 if the last three digits are divisible by 8. For example: 12816(816 is exactly divisible by 8) hence this number is exactly divisible by 8.

## Rules (numbers 9,10,11,12,15,19,25)

• A number is divisible by 9 if the sum of all of its digits is completely divisible by 9. For example 1295874(the sum of its digits 1+2+9+5+8+7+4=36/9=4) hence this number is completely divisible by 9.
• A number is divisible by 10 if the digit at unit’s place is zero. For example:12580 , this number is exactly divisible by 0,because unit’s place digit is 0.
• A number is divisible by 11 if difference between the sum of digits at odd place and sum of digits at even place is 0 or 11. For example:2332(odd place=2+3=5, even place 2+3=5 so 5-5=0) hence the number is exactly divisible by 11.
• A number is divisible by 12 if the number is divisible by both 3 and 4. For example:2268(this number is divisible by both 3 and 4), hence this number is completely divisible by 12.
• A number is divisible by 15 if it is divisible by both 3 and 5. For example:1605(this number is divisible by both 3 and 5) hence this number is divisible by 15.
• A number is divisible by 19 if the sum of digits other than unit digit and twice of unit’s digit is divisible by 19. For example:76(7+2*6=19/19=1) hence this number is completely divisible by 19.
• A number is divisible by 25 if its last two digits are divisible by 25. For example: 1225(the last two digits are divisible by 25), so this number is divisible by 25.

## Quantitative Aptitude – Some key points of Number System

• 0 is not a natural number.
• o is neither positive number nor negative number.Therefore this number is known as neutral number.
• 2 is the only even prime number.
• The sum of 1st n natural numbers=n(n+1)/2
• sum of 1st n even numbers=n(n+1)
• The sum of 1st n odd numbers=n2
• The sum of square of first n natural numbers=n(n+1)(2n+1)/6

In the next post, we will discuss LCM and HCF. If you have any doubts or concern then you can mail us on [email protected]