Topics
Number System(Consolidating the Sense of Numberness)
Number System
Estimation
Ratio and Proportion
Numbers in India and International System (With Comparison)
Algebra
Geometry
Place Value
Mensuration
Natural Numbers and Whole Numbers (Including Patterns)
Negative Numbers and Integers
Data Handling
Number Line
HCF and LCM
Playing with Numbers
- Simplification of Brackets
- Finding Factors Using Rectangular Arrangements and Division
- Factors and Common Factors
- Multiples and Common Multiples
- Concept of Even and Odd Number
- Tests for Divisibility of Numbers
- Divisibility by 2
- Divisibility by 4
- Divisibility by 8
- Divisibility by 3
- Divisibility by 6
- Divisibility by 9
- Divisibility by 5
- Divisibility by 11
Sets
Ratio
Proportion (Including Word Problems)
Unitary Method
Fractions
- Concept of Fraction
- Types of Fractions
- Concept of Proper and Improper Fractions
- Concept of Mixed Fractions
- Like and Unlike Fraction
- Concept of Equivalent Fractions
- Conversion between Improper and Mixed fraction
- Conversion between Unlike and Like Fractions
- Simplest Form of a Fractions
- Comparing Fractions
- Addition of Fraction
- Subtraction of Fraction
- Multiplication of Fraction
- Division of Fractions
- Using Operator 'Of' with Multiplication and Division
- BODMAS Rule
- Problems Based on Fraction
Decimal Fractions
Percent (Percentage)
Idea of Speed, Distance and Time
Fundamental Concepts
Fundamental Operations (Related to Algebraic Expressions)
Substitution (Including Use of Brackets as Grouping Symbols)
Framing Algebraic Expressions (Including Evaluation)
Simple (Linear) Equations (Including Word Problems)
Fundamental Concepts
Angles (With Their Types)
Properties of Angles and Lines (Including Parallel Lines)
Triangles (Including Types, Properties and Constructions)
Quadrilateral
Polygons
The Circle
Symmetry (Including Constructions on Symmetry)
Recognition of Solids
Perimeter and Area of Plane Figures
Data Handling (Including Pictograph and Bar Graph)
Mean and Median
- Definition: Prime Numbers
- Definition: Twin Prime Numbers
- Definition: Composite Number
- Activity: Prime or Composite? Build and Decide!
- Classification of Numbers Based on Their Factors
- Key Points Summary
Definition: Prime Numbers
A prime number is a natural number greater than 1 that has exactly two factors: 1 and the number itself.
2, 3, 5, 7, 11, and so on are examples of prime numbers.
Definition: Twin Prime Numbers
If the difference between two coprime numbers is 2, the numbers are said to be twin prime numbers. For example: (3, 5)
Definition: Composite numbers
Numbers having more than two factors are called composite numbers. 4, 6, 8, 9, 10, and so on are examples of composite numbers.
Prime or Composite? Build and Decide!
Step 1: Guna arranges 12 figs
Guna tries to arrange 12 figs in different rectangular shapes.
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Arrangement 1: 1 × 12
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Arrangement 2: 2 × 6
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Arrangement 3: 3 × 4
He finds 3 different rectangular arrangements.
Step 2: Anshu arranges 7 figs
Anshu tries to arrange 7 figs in rectangles.
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Arrangement: 1 × 7
She finds only one rectangular arrangement.
Conclusion:
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If a number can form many rectangular arrangements, it has many factors → it is composite (like 12).
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If a number can form only one rectangular arrangement, it has only two factors → it is prime (like 7).
- Number of arrangements = Number of factor pairs.
Classification of Numbers Based on Their Factors
|
Numbers |
Factors |
Number of Factors |
| 1 | 1 | 1 |
| 2 | 1, 2 | 2 |
| 3 | 1, 3 | 2 |
| 4 | 1, 2, 4 | 3 |
| 5 | 1, 5 | 2 |
| 6 | 1, 2, 3, 6 | 4 |
| 7 | 1, 7 | 2 |
| 8 | 1, 2, 4, 8 | 4 |
| 9 | 1, 3, 9 | 3 |
| 10 | 1, 2, 5, 10 | 4 |
| 11 | 1, 11 | 2 |
| 12 | 1, 2, 3, 4, 6, 12 | 6 |
- The number 1 has only one factor (i.e., itself).
- 1 is neither a prime nor a composite number.
- There are numbers having more than two factors like 4, 6, 8, 9, 10, and so on. These numbers are composite numbers.
Key Points Summary
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A prime number has exactly two factors.
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1 is neither prime nor composite.
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Twin primes come in pairs, two apart.
