A number system is defined as a systematic way of expressing numbers. The number system is a mathematical notation for representing numbers of a given set by using a set of digits or symbols in a logical manner. Number System helps to understand the basics of quantitative ability.

**The value of any specific digit in a number can be determined by**

- The actual digit
- Its position in the number
- The base of the number system

**Classification of Numbers:**

The number system is classified into following types:

**Natural Numbers:**

Numbers which are used for counting objects are known as Natural numbers. The natural numbers are denoted by N.

N = {1, 2, 3, 4…………}

**Whole Numbers:**

Whole numbers are the set of numbers in which zero is included in addition to natural numbers. The whole numbers are denoted by W.

W = {0, 1, 2, 3, 4…….}

**Integers:**

Integers include all natural numbers in addition to zero & negative numbers. Integers are denoted by I or Z.

I = {-3, -2, -1, 0, 1, 2, 3…..}

**Rational Numbers:**

Rational numbers are expressed in the form of p/q where ‘p’ & ‘q’ are integers and q≠0. They are denoted by Q.

Q = 5/6, 7/8 etc.

**Irrational Numbers:**

The numbers which cannot be expressed in the form of p/q where ‘p’ & ‘q’ are integers and q≠0. They are denoted by Q.

Example - π = 3.141592653589793238….

**Prime Numbers:**

A prime number is a natural number which is divisible only by 1 and itself. It is greater than 0.

Example - 2, 3, 5, 7, 11, 31, etc.

**Composite Numbers:**

All the numbers (except 1) which do not fall under the category of prime numbers are known as composite numbers.

Example - 4, 8, 10, 22, 100 etc.

**Co-Prime Numbers:**

Co-Prime Numbers are the set of integers which have only 1 as their common factor or the highest common factor (HCF) is 1.

Example – 13 & 14 are co-prime.

**Even Numbers:**

The numbers which are divisible by 2 are known as even numbers.

Example – 2, 4, 6, 8, 10….

**Odd Numbers:**

The numbers which are not divisible by 2 are known as odd numbers.

Example – 3, 5, 7, 9……

**Tricks to remember while solving number system questions:**

- 1 is neither divisible nor prime.
- Two consecutive odd prime numbers are known as prime pair.
- All natural numbers are whole, integer, rational and real.
- All whole numbers are rational, Integer and real.
- All rational numbers incorporates integers, since every integer can be written as a fraction with denominator 1. Example (9/1).
- The square of an even is even and the square of an odd number is odd.
- Any given Prime Number can never be a Composite Number.
- Fractions are rational.
- Zero is neither negative nor positive number.
- If x is any number then, if x divides zero, result will be zero. If 0 divides x, then result will be infinite or not defined or undetermined i.e. 0/x =0, but x/0 =∞ (infinite) where x is real number.
- The sum and the product of two rational number is always a rational numbers.
- The product or the sum of a rational number and irrational number is always an irrational number.

Examples:

Q1: Is 881 a Prime Number?

Ans: The approximate square root of 881 is 30. Prime numbers less than 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 etc.

Q2: Which of the following are Co-Prime Number?

1) (2,8)

2) (4,5)

3) (9,12)

4) (12,15)

5) None of these

Answer: Option 2, only positive integer (factor) that divides both of them is 1.

Q3: Which number is neither Prime nor Composite?

1) 11

2) 40

3) 18

4) 1

5) None of these

Answer: Option 4. 1 is neither prime nor composite.

Q4: Consider the following statement: All Prime numbers are Odd.

1) True

2) False

3) True except 2

4) False except 2

5) None of the above

Answer: Option 3.

Q5: Which number is Rational but not Integer?

1) 7

2) 0

3) 8

4) 2.5

5) Pie (π)

Answer: Option 4.

**Number System: Frequently Asked Questions**

Q1: What is Number System?

Answer: Number System is the basic topic of mathematics. Number System helps to understand the basics of quantitative ability.

Q2: In which exams questions related number system are asked?

Answer: Questions related to number system are asked in quantitative aptitude section of all competitive exams like IBPS, SSC, Railways, CSAT etc.

Q3: How many questions are asked from number system?

Answer: On an average, 1-2 questions are asked from number system.

Q4: How can I solve Number System questions?

Answer: Practice is the key. Go through the concepts mentioned above & start solving questions.

Number System Shortcuts & Tricks For Bank Exams?

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