SSC CGL Maths: Classification of Numbers – Complete Guide in Hinglish (Hindi +English)

Note: Ye article specially SSC CGL, OSSC CGL aur baaki government exams ke liye design kiya gaya hai. Hinglish language use ki gayi hai taaki beginner bhi easily samajh sake.

Introduction: Numbers Ka Duniya

Namaste dosto! Aaj ham SSC CGL ke sabse important topic se start kar rahe hain – Classification of Numbers. Agar aap maths mein zero level se padhna chahte ho, toh ye post aapke liye bilkul perfect hai.

Kisi bhi government exam (SSC CGL, OSSC CGL, Bank, Railway, State Exams, etc.) mein Number System bahut hi important chapter hota hai. Aur Number System ka foundation hai Classification of Numbers.

Numbers Kya Hote Hain?

Numbers wo mathematical values hote hain jinhe hum counting (ginnati) aur measuring (maapna) ke liye use karte hain. Jaise: 1, 2, 3, -5, 0.5, √2, π, etc.

Itne saare numbers ko samajhne ke liye unko groups mein baanta jaata hai. Is process ko hi hum bolte hain Classification of Numbers.

Exam Point of View: Number System se almost har competitive exam me questions aate hain – direct identification, properties based questions, ya application based problems.

1. NATURAL NUMBERS (N)

Definition

Natural Numbers wo positive integers hote hain jo 1 se start hote hain aur infinity tak jaate hain. Inhe hum generally counting numbers bhi kehte hain.

N = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... }

Important Characteristics

Sabse chhota natural number = 1
Koi bhi sabse bada natural number nahi hota (set infinite hai)
Natural numbers hamesha positive hote hain
0 natural number nahi hai
Negative numbers natural numbers me include nahi hote

Examples

✓ 5, 10, 100, 9999, 50000 (sab natural numbers)
✗ 0, -5, -10, 3.5 (natural numbers nahi hain)

Real Life Examples

Aapke paas kitni kitaabe hain? – 5 books (Natural number)
Class mein kitne students hain? – 60 students (Natural number)
Cricket team me players – 11 players (Natural number)

2. WHOLE NUMBERS (W)

Definition

Whole Numbers basically Natural Numbers hote hain, lekin inme 0 bhi include hota hai.

W = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... }

Key Points

Natural Numbers + 0 = Whole Numbers
Sabse chhota whole number = 0
Whole numbers bhi hamesha non-negative hote hain
Negative numbers whole numbers nahi hote

Natural vs Whole Numbers

Feature	Natural Numbers	Whole Numbers
Starting Point	1	0
Contains Zero	✗ Nahi	✓ Haan
Examples	1, 2, 3, 4...	0, 1, 2, 3...
Smallest Number	1	0

Real Life Examples

Pocket me paise: 0 rupee (whole number)
Empty box me chocolates: 0 chocolate

3. INTEGERS (Z)

Definition

Integers wo numbers hote hain jisme negative numbers, zero aur positive numbers sab aate hain.

Z = { ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }

Key Points

Integers = Negative Numbers + Zero + Positive Numbers
Integers ke fractional/decimal part nahi hote
Symbol: Z (German word “Zahlen” se)

Types of Integers

Positive Integers: 1, 2, 3, 4, 5... (Natural numbers)
Negative Integers: -1, -2, -3, -4, -5...
Zero: 0 (na positive, na negative)

Whole vs Integers

Feature	Whole Numbers	Integers
Negative Numbers	✗ Nahi	✓ Haan
Zero	✓ Haan	✓ Haan
Positive Numbers	✓ Haan	✓ Haan
Examples	0, 1, 2, 3...	..., -2, -1, 0, 1, 2...

Real Life Examples

Bank balance: +5000 rupee (positive integer)
Temperature: -5°C (negative integer)
Building ka ground floor: 0

4. EVEN NUMBERS

Definition

Even Numbers wo numbers hote hain jo 2 se completely divide hote hain, yani remainder 0 aata hai.

Even Numbers = { 0, 2, 4, 6, 8, 10, 12, 14, 16, ... }

General Form: 2n (jahan n koi bhi integer hai)

Characteristics

Last digit hamesha 0, 2, 4, 6, ya 8 hota hai
2 se divide karne par remainder = 0
Negative even numbers bhi hote hain: -2, -4, -6...

Quick Check

248 → last digit 8 → Even ✓
357 → last digit 7 → Even nahi (Odd)

5. ODD NUMBERS

Definition

Odd Numbers wo numbers hote hain jo 2 se divide nahi hote, yani remainder 1 aata hai.

Odd Numbers = { 1, 3, 5, 7, 9, 11, 13, ... }

General Form: 2n + 1

Characteristics

Last digit hamesha 1, 3, 5, 7, ya 9
2 se divide karne par remainder = 1
Negative odd numbers bhi hote hain: -1, -3, -5...

Even vs Odd

Property	Even	Odd
Divisible by 2	✓ Yes	✗ No
Last Digit	0, 2, 4, 6, 8	1, 3, 5, 7, 9
General Form	2n	2n + 1
Remainder on ÷ 2	0	1

6. PRIME NUMBERS

Definition

Prime Numbers wo natural numbers hote hain jinke sirf 2 factors hote hain:

1
Wo number khud

Important Points

1 prime nahi hai (sirf 1 factor)
2 sabse chhota aur eklauta even prime number hai
Prime numbers infinite hote hain

Prime Numbers (100 tak)

2, 3, 5, 7, 11, 13, 17, 19, 23, 29,
31, 37, 41, 43, 47,
53, 59, 61, 67, 71,
73, 79, 83, 89, 97

Prime Check – Example

Q: Kya 29 prime hai?

√29 ≈ 5.4
5 se chhote primes: 2, 3, 5
29 ÷ 2, 3, 5 – kisi se bhi completely divide nahi hota

Isliye 29 prime number hai.

7. COMPOSITE NUMBERS

Definition

Composite Numbers wo natural numbers hote hain jinke 2 se zyada factors hote hain.

Key Points

1 composite nahi hai
Sabse chhota composite number = 4
Composite numbers ke kam se kam 3 factors hote hain

Prime vs Composite

Property	Prime	Composite
Number of Factors	Exactly 2	More than 2
Smallest Number	2	4
Examples	2, 3, 5, 7, 11...	4, 6, 8, 9, 10...

8. RATIONAL NUMBERS (Q)

Definition

Rational Numbers wo hote hain jo p/q form me likhe ja sakte hain, jahan:

p = koi bhi integer
q = koi bhi integer (q ≠ 0)

Rational Number = p/q, jahan p, q ∈ Integers aur q ≠ 0

Examples

✓ 1/2, 3/4, 7/5, -3/2, 5, 0 (sab rational hain)
✗ √2, π, √3 (irrational)

Decimal Form

Terminating: 1/2 = 0.5, 1/4 = 0.25
Repeating: 1/3 = 0.333..., 2/3 = 0.666...

9. IRRATIONAL NUMBERS

Definition

Irrational Numbers wo numbers hote hain jo p/q form me likhe hi nahi ja sakte, jahan p aur q integers hon.

Key Points

Decimal expansion non-terminating aur non-repeating hoti hai
Fraction form (integer p/q) me exact convert nahi ho sakte

Examples

✓ π, √2, √3, √5, e (irrational)
✗ 1/2, 0.5, 0.333... (rational)

10. REAL NUMBERS (R)

Definition

Real Numbers me saare rational + irrational numbers include hote hain.

Real Numbers (R) = Rational Numbers (Q) + Irrational Numbers

Examples

✓ 5, -7, 3/4, 0, √2, π, e (sab real numbers)
✗ 2i, 3 + 4i (complex, real nahi)

Number Tree (Text Form)

REAL NUMBERS (R)
/ \
/ \
RATIONAL (Q) IRRATIONAL
/ | \
INTEGER FRACTION DECIMAL
/ | \
W 0 Negative
|
NATURAL

Summary Table – Sab Ek Jagah

Type	Definition	Examples	Important Point
Natural (N)	1 se start hone wale positive integers	1, 2, 3, 4...	0 include nahi hota
Whole (W)	Natural + 0	0, 1, 2, 3...	Smallest whole = 0
Integer (Z)	Negative + 0 + Positive	..., -2, -1, 0, 1, 2...	No fractions/decimals
Even	2 se divisible	0, 2, 4, 6...	Last digit 0,2,4,6,8
Odd	2 se divisible nahi	1, 3, 5, 7...	Last digit 1,3,5,7,9
Prime	Exactly 2 factors	2, 3, 5, 7...	1 prime nahi, 2 only even prime
Composite	2 se zyada factors	4, 6, 8, 9...	Smallest composite = 4
Rational (Q)	p/q form, q ≠ 0	1/2, -3/4, 5	Decimal terminating/repeating
Irrational	p/q form possible nahi	π, √2, √3	Decimal non-terminating & non-repeating
Real (R)	Rational + Irrational	Sab above wale	Complex exclude

FAQs – Students Ke Common Doubts

Q. Kya 0 natural number hai?
Nahi, 0 natural number nahi hai. Natural numbers 1 se start hote hain. Lekin 0 whole number hai.

Q. Kya 1 prime number hai?
Nahi, 1 prime nahi hai kyunki prime ke 2 factors hone chahiye. 1 ka sirf ek factor hai – 1 khud.

Q. Sabse chhota prime number kaun sa hai?
2 sabse chhota prime number hai, aur ye hi eklauta even prime number hai.

Q. Kya har integer rational number hota hai?
Haan, kyunki har integer n ko n/1 form me likh sakte hain.

Q. Negative numbers prime ho sakte hain?
Nahi, prime numbers definition natural numbers par based hai, jo positive hote hain.

Practice Questions – Khud Try Karo

97 prime hai ya composite?
-5 kaun sa type ka number hai? (integer / rational / real?)
0.333... (repeating) rational hai ya irrational?
√4 aur √5 me se kaun irrational hai?
Sabse chhota composite number kaun sa hai?

Next Chapter Idea: Agar tum bolo to next post me Prime Factorization, HCF, LCM aur Divisibility Rules ko isi style me detail se cover kara ja sakta hai.