Infographics Number System - Quantitative Aptitude for SSC CGL PDF Download

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Number System: A Complete 
Visual Guide
Numbers form the foundation of all mathematical reas oning and play a vital role in every aspect 
of our lives4from daily calculations to complex probl em-solving. This comprehensive 
infographic explores the different types of numbers, their classifications, and the essential 
concepts you need to master for entrance exams like SSC CGL.
What is a Number?
A number is a mathematical concept used for 
counting, measuring, or labelling things. 
Numbers play a key role in arithmetic 
calculations and come in various types.
They can be classified as even or odd based 
on divisibility by 2, and as prime or 
composite depending on the number of 
factors.
In number systems, numbers serve as digits. 
Binary uses 0 and 1, whilst other systems use 
digits from 0 to 9. Understanding various 
types of numbers and their systems is 
essential in mathematics and competitive 
examinations.
Classification of Numbers
Real Numbers
Include rational and irrational numbers. 
Can be located on the number line. 
Examples: -3/4, 5/2, Ã, :2
Imaginary Numbers
Involve the imaginary unit "i" where i² = 
-1. Complex numbers combine real and 
imaginary components: a + bi
Rational Numbers
Real numbers in the form p/q where q b 0. 
Examples: 1/2, 1/5, 3/4
Irrational Numbers
Cannot be expressed as ratios. Non-
repeating, non-terminating decimals. 
Examples: Ã, :2
Types of Numbers
Integers (Z)
Set including all whole 
numbers and their negatives: 
{..., -3, -2, -1, 0, 1, 2, 3, ...}
Negative integers: Z{ = 
{-1, -2, -3...}
Neutral: Zero (0)
Positive integers: Zz = {1, 
2, 3...}
Natural Numbers (N)
The counting numbers: N = {1, 
2, 3, 4, 5...}. All positive 
integers are natural numbers, 
providing infinite natural 
numbers.
Whole Numbers (W)
All natural numbers together 
with '0': W = {0, 1, 2, 3...}. 
Also known as non-negative 
integers.
Even, Odd, and Prime Numbers
Even Numbers
Divisible by 2. Can be 
expressed as 2n where n is 
an integer.
Examples: 2, 4, 6, 8, 10, -2, 
-6
Odd Numbers
Not divisible by 2. Can be 
expressed as (2n + 1) where 
n is an integer.
Examples: 1, 3, 5, 7, 9, -3, -5
Prime Numbers
Natural numbers with only 
two factors: itself and unity.
Examples: 2, 3, 5, 7, 11, 13, 
17, 19
Prime Number Facts
Key Properties
2 is the lowest and only even prime 
number
3 is the lowest odd prime number
Prime p g 5 divided by 6 leaves 
remainder 1 or 5
For prime p > 3, p² - 1 is divisible by 
24
Must Know Counts
1 to 25 ó 9 prime numbers
1 to 50 ó 15 prime numbers
1 to 100 ó 25 prime numbers
1 to 200 ó 45 prime numbers
Testing for Prime Numbers
Step 1: Find Square Root
Calculate the square root of the number N 
and round up to the next integer (z).
Step 2: List Prime Numbers
Identify all prime numbers less than or 
equal to z.
Step 3: Check Divisibility
Test if N is divisible by any prime number 
from the list.
Step 4: Determine Result
If no prime divides N, then N is a prime 
number.
Divisibility Rules
Divisibility by 2
If the last digit is even (0, 2, 4, 6, 8), 
the number is divisible by 2.
Divisibility by 3
If the sum of digits is divisible by 3, the 
number is divisible by 3.
Divisibility by 4
If the last two digits form a number 
divisible by 4, the entire number is 
divisible by 4.
Divisibility by 5
If the last digit is 0 or 5, the number is 
divisible by 5.
Divisibility by 9
If the sum of digits is divisible by 9, the 
number is divisible by 9.
Divisibility by 11
If the difference between sum of 
alternate digits is divisible by 11, the 
number is divisible by 11.
HCF and LCM
Highest Common Factor 
(HCF)
The highest factor common to two or more 
numbers. Also called GCD (Greatest 
Common Divisor).
Example: HCF of 96, 36, and 18
96 = 2u × 3
36 = 2² × 3²
18 = 2 × 3²
HCF = 2 × 3 = 6
Least Common Multiple 
(LCM)
The smallest number exactly divisible by all 
given numbers. Product of highest powers of 
all prime factors.
Example: LCM of 96, 36, and 18
96 = 2u × 3
36 = 2² × 3²
18 = 2 × 3²
LCM = 2u × 3² = 288
Important Relationship
For any two numbers A and B:
A × B = H C F ( A , B ) × L C M ( A , B )
Remainders and Cyclicity
Remainder Basics
When M is divided by N: 
Dividend = Quotient × 
Divisor + Remainder
Remainder is always less 
than the divisor.
Cyclicity Concept
Unit digits repeat in 
patterns. Digits 2, 3, 7, 8 
have a cycle of 4. Digits 
4, 9 have a cycle of 2.
Trailing Zeroes
In factorials, count the 
number of 5s. For n!, 
divide n by 5 repeatedly 
and sum quotients.
Cyclicity Table
0, 1, 5, 6 Cycle of 1 Same digit always
4, 9 Cycle of 2 4: {4, 6}, 9: {9, 1}
2, 3, 7, 8 Cycle of 4 2: {2,4,8,6}, 3: {3,9,7,1}
Quick Reference Formulas
Perfect Numbers
Sum of factors 
(excluding itself) equals 
the number.
Example: 6 = 1 + 2 + 3
Co-Prime 
Numbers
Two numbers with HCF = 
1 are co-prime.
Example: 8 and 9
Composite 
Numbers
Numbers with more than 
two factors.
Note: 1 is neither prime 
nor composite
Practice Tips for Success
1
Master Divisibility 
Rules
Memorise and practise 
divisibility rules for 
numbers 2-13. Use 
mnemonics like "Even 2, 
Sum 3, Last-two 4, Zero-
five 5" for quick recall.
2
Understand 
Patterns
Recognise cyclicity 
patterns in unit digits. 
Practise calculating 
remainders using negative 
remainder concepts for 
faster solutions.
3
Solve Regularly
Work through examples 
daily. Start with easy 
problems, then progress 
to medium and hard 
difficulty levels to build 
confidence.
Common Pitfalls to Avoid
¦ Calculation Errors
For 3 or 9, check sum of digits, not 
product
For 7, follow exact steps to avoid mistakes
Remember remainder is always less than 
divisor
¦ Conceptual Mistakes
Don't confuse HCF with LCM
Remember 1 is neither prime nor 
composite
Check if numbers are co-prime before 
applying rules
Key Takeaways
Foundation is 
Crucial
Number system 
concepts form the 
basis for all 
quantitative aptitude 
topics. Master these 
fundamentals before 
moving to advanced 
topics.
Practice Makes 
Perfect
Regular practice with 
diverse problem types 
builds speed and 
accuracy. Focus on 
both conceptual 
understanding and 
calculation techniques.
Shortcuts Save 
Time
Learn and apply 
shortcuts for 
divisibility, HCF/LCM, 
and remainders. Time 
management is critical 
in competitive 
examinations like SSC 
CGL.
"Numbers are the foundation of mathematics. Understan ding their properties, classifications, 
and relationships unlocks the door to success in qu antitative aptitude and beyond."
This comprehensive guide covers all essential concepts in the Number System for SSC CGL 
preparation. Revise regularly, practise diverse problems, and apply shortcuts strategically to 
maximise your performance in the examination. Remember, consistent effort and conceptual 
clarity are your keys to success!