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Chapter 3 – Playing with Numbers

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

Numbers are an inherent part of our every-day life and continue to remain an important factor through which we measure things. Numbers are used extensively in the business and finance domain, along with other instruments of life. Let’s check the different concepts of playing with numbers, along with their various operational characteristics in this article.

Factors are the exact divisors of any number that leave no remainder. For example, if we take 12 as our number. Then we can find multiple numbers as their exact divisor. They are as follows: 1, 2, 3, 4, 12, and 6.

Let’s check some properties of factors:

  • Any number is a factor of itself.
  • 1 is always an integral factor of any number. 
  • Factors are always lesser than, or equal to the number, and never greater than it.
  • There can be a finite number of factors for any given number.

Multiples are the multiplicative values of any given numbers. Hence, we multiply the given number with a natural number to obtain their multiples. For example, we have the number 3, and we need to calculate its multiples. Then we start multiplying 3 with natural numbers starting from 1. Hence we get 3, 6, 9, 12, 15, 18, and more.

  • Every multiple of a number is always equal to, or greater than that number.
  • There can be an infinite number of multiples of any given number as we can keep on multiplying till infinity.
  • Every number is a multiple of itself.

Suppose we are given more than two numbers and told to find their factors and multiples. Then, we can get some common factors and common multiples for every given number.

Prime Numbers: Any number other than 1 with only two factors, the number itself and 1, are called prime numbers. Examples: 2, 3, 5, 7, and more. All these numbers have exactly two factors that are the number itself and 1.

Composite numbers: If any given pair of numbers has more than two factors, they are called composite numbers. For examples 12, 14, 15, and more. All these numbers have at-least 3 factors and hence are called composite numbers.

We can test the divisibility rules based on some predefined rules for the existing numbers. Let’s check for the divisibility test of numbers according to the rules that are given below:

NumberDivisibility Rule
2Any number with 0, 4, 2, 6, and 8 at its one’s place is divisible by 2.
3If the sum of the given number’s digits is divisible by 3, that number is divisible by 3.
4For numbers having more than 3 digits, check the divisibility of the last two-digit by 4.
5If the last digit is 0 or 5, then the number is divisible by 5.
6Any number has to satisfy this condition of being divisible by both 2 and 3 to be divisible by 6.
10If the last digit of the number is 0, then the number is divisible by 10.

The factorisation is the method to break down the number in terms of its factors. Prime factorisation is similar to factorisation, with the only difference being that the factors are prime numbers. For example, if we have 36 to be factored, then the answer will be 36 = 2 * 2 * 3 * 3. Hence 2 and 3 are prime numbers here. Some problems consist of large numbers that have to be factored using prime factorisation. For that, we have a different tabular method of prime factorisation.

When we are given two numbers, we can do their prime factorisation. Then the highest common factor of the set two numbers is the HCF of the pair of numbers. It is also known as the greatest common factor.

For example, if we have 12 and 24 as our numbers. Now after prime factorisation, we get,

  • 12 = 2 * 2 * 3
  • 24 = 2 * 2 * 2 * 3

Here, the common multiples are 2 * 2 *3 = 12. Hence, 12 is the HCF of 12 and 24.

It is the lowest common multiple of any two given numbers. For example, if we have two number as 12 and 24, that after factorisation we get:

  • 12 = 2 * 2 * 3 
  • 24 = 2 * 2 * 2 * 3

Now in this the common multiples are 2 * 2 * 3 = 12. Also, there is one uncommon multiple, i.e., 2. So, 12 * 2 = 24. Hence, 24 is their least common multiple.

Playing with Numbers is an important maths topic and is an inherent part of mathematics and human life. In this topic, we saw the different concepts that can be used on numbers. We can see factors, multiples, prime numbers, odd-even numbers and more in this topic. We can also check for test for divisibility of numbers using certain rules.

  1. What do you mean by playing with numbers?

Playing with Numbers is an 8th class NCERT maths chapter that deals with numbers’ various properties and characteristics.

  1. How do you teach numbers to play?

Numbers are the base of mathematics and should be taught to small children through fun activities.

  1. What are whole numbers for Class 6?

Whole numbers are the counting numbers that are positive and start from zero. They can be depicted on the number line.

  1. What is a Co-prime number?

The pair of numbers having 1 as their highest common Factor is known as co-primes. Co-primes are always formed for pairs. E.g., 1 and 22

  1. What is the meaning of Factor?

Factors are exact divisors of those numbers that leave no remainder. For example, the factors of 12 are 1, 2, 3, 4, and 6.

  1. What is the smallest Co-prime number?

The smallest coprime numbers are 1 and 2.

Download MSVgo to know more about numbers and the different types of numbers that play an important role in beginning the base of mathematics. You can get video tutorials that explain the topic well.

High School Physics

  • Alternating Current
  • Atoms
  • Communication Systems
  • Current Electricity
  • Dual nature of Radiation and Matter
  • Electric Charges and Fields
  • Electricity
  • Electromagnetic Induction
  • Electromagnetic Waves
  • Electron Beams and Radioactivity
  • Electrons and Photons
  • Electrostatic Potential and Capacitance
  • Fluid Pressure
  • Force and Acceleration
  • Force And Laws Of Motion
  • Gravitation
  • Internal Energy
  • Kinetic Theory
  • Law of motion
  • Light – Reflection And Refraction
  • Magnetic Effects Of Electric Current
  • Magnetism and Matter
  • Management Of Natural Resources
  • Mechanical properties of Fluids
  • Mechanical properties of Solids
  • Motion
  • Motion in a plane
  • Motion in a straight line
  • Moving Charges and Magnetism
  • Nuclear Energy
  • Nuclei
  • Oscillations
  • Our Environment
  • Paths of Heat
  • Physical world
  • Ray optics and optical instruments
  • Semiconductor Devices
  • Semiconductor Electronics: Materials, Devices and Simple Circuits
  • Simple Machines
  • Sound
  • Sources Of Energy
  • Specific and Latent Heats
  • Spherical Mirrors
  • Static Electricity
  • Systems of Particles and Rotational motion
  • Thermal properties of matter
  • Thermodynamics
  • Units and Measurement
  • Vectors, Scalar Quantities and Elementary Calculus
  • Wave Optics
  • Waves
  • Work, Power and Energy

High School Chemistry

  • Acids, Bases and Salts
  • Alcohols, Phenols and Ethers
  • Aldehydes, Ketones and Carboxylic Acids
  • Aliphatic and Aromatic Hydrocarbons
  • Alkyl and Aryl Halides
  • Amines
  • Analytical Chemistry 
  • Atomic Structure
  • Atoms And Molecules
  • Basic concepts of Chemistry
  • Biomolecules
  • Carbon And Its Compounds
  • Carboxylic acids and Acid Derivatives
  • Chemical Bonding and Molecular Structures
  • Chemical Energetics
  • Chemical Equilibria
  • Chemical Kinetics
  • Chemical Reactions And Equations
  • Chemical Reactions and Their Mechanisms
  • Chemistry in Everyday Life
  • Chemistry of p-Block elements
  • Chemistry of Transition and Inner Transition
  • Classification of Elements
  • Coordination Compounds
  • Cyanide, Isocyanide, Nitro compounds and Amines
  • Electrochemistry
  • Electrolysis
  • Elements, Compounds and Mixtures
  • Environmental Chemistry
  • Equilibrium
  • Ethers and Carbonyl compounds
  • Haloalkanes and Haloarenes
  • Hydrocarbons
  • Hydrogen
  • Ideal solutions
  • Introduction to Organic Chemistry
  • Ionic equilibria
  • Matter
  • Matter Around Us
  • Matter In Our Surroundings
  • Metallurgy
  • Metals And Non-Metals
  • Mole Concept and Stoichiometry
  • Natural Resources
  • Organic Chemistry – Basic Principles
  • Periodic Classification of Elements
  • Physical and Chemical Changes
  • Physical and Chemical Properties of Water
  • Polymers
  • Preparation, Properties and Uses of Compounds
  • Principles and Processes of Isolation of Elements
  • Redox Reactions
  • Relative Molecular Mass and Mole
  • States of Matter
  • Structure Of The Atom
  • Study of Compounds
  • Study of Gas Laws
  • Study of Representative Elements
  • Surface Chemistry
  • The d-block and f-block elements
  • The Gaseous State
  • The p-Block Elements
  • The Periodic Table
  • The s-Block Elements
  • The Solid State
  • Thermodynamics

High School Biology

  • Absorption and Movement of Water in Plants
  • Adolescent Issues
  • Anatomy of Flowering Plants
  • Animal Kingdom
  • Bacteria and Fungi-Friends and Foe
  • Biodiversity and Conservation
  • Biofertilizers
  • Biological Classification
  • Biomedical Engineering
  • Biomolecules
  • Biotechnology and its Applications
  • Biotic Community
  • Body Fluids and Circulation
  • Breathing and Exchange of Gases
  • Cell – Unit of Life
  • Cell Cycle and Cell Division
  • Cell Division and Structure of Chromosomes
  • Cell Reproduction
  • Cellular Respiration
  • Chemical Coordination and Integration
  • Circulation
  • Control And Coordination
  • Crop Improvement
  • Digestion and Absorption
  • Diversity In Living Organisms
  • Ecosystem
  • Environmental Issues
  • Excretory Products and their Elimination
  • Flowering Plants
  • Genes and Chromosomes
  • Health and Diseases
  • Health and Its Significance
  • Heredity And Evolution
  • Heredity and Variation
  • How Do Organisms Reproduce?
  • Human Diseases
  • Human Eye And Colourful World
  • Human Health and Disease
  • Human Population
  • Human Reproduction
  • Hygiene
  • Improvement In Food Resources
  • Integumentary System- Skin
  • Kingdom Fungi
  • Kingdom Monera
  • Kingdom Protista
  • Life Processes
  • Locomotion and Movement
  • Microbes in Human Welfare
  • Mineral Nutrition
  • Molecular Basis of Inheritance
  • Morphology of Flowering Plants
  • Neural Control And Coordination
  • Nutrition in Human Beings
  • Organism and Population
  • Photosynthesis
  • Photosynthesis in Higher Plants
  • Plant Growth and Development
  • Plant Kingdom
  • Pollination and Fertilization
  • Pollution; Sources and its effects
  • Principles of Inheritance and Variation
  • Reproduction and Development in Angiosperms
  • Reproduction in Organisms
  • Reproductive Health
  • Respiration in Human Beings
  • Respiration in Plants
  • Respiratory System
  • Sexual Reproduction in Flowering Plants
  • Strategies for Enhancement in Food Production
  • Structural Organisation in Animals
  • Structural Organisation of the Cell
  • The Endocrine System
  • The Fundamental Unit Of Life
  • The Living World
  • The Nervous System and Sense Organs
  • Tissues
  • Transpiration
  • Transport in Plants

High School Math

  • Algebra – Arithmatic Progressions
  • Algebra – Complex Numbers and Quadratic Equations
  • Algebra – Linear Inequalities
  • Algebra – Pair of Linear Equations in Two Variables
  • Algebra – Polynomials
  • Algebra – Principle of Mathematical Induction
  • Algebra – Quadratic Equations
  • Binomial Theorem
  • Calculus – Applications of Derivatives
  • Calculus – Applications of the Integrals
  • Calculus – Continuity and Differentiability
  • Calculus – Differential Equations
  • Calculus – Integrals
  • Geometry – Area
  • Geometry – Circles
  • Geometry – Conic Sections
  • Geometry – Constructions
  • Geometry – Introduction to Euclid’s Geometry
  • Geometry – Three-dimensional Geometry
  • Geometry – Lines and Angles
  • Geometry – Quadrilaterals
  • Geometry – Straight Lines
  • Geometry – Triangles
  • Linear Programming
  • Matrices and Determinants
  • Mensuration – Areas
  • Mensuration – Surface Areas and Volumes
  • Number Systems
  • Number Systems – Real Numbers
  • Permutations and Combinations
  • Probability
  • Sequence and Series
  • Sets and Functions
  • Statistics 
  • Trignometry – Height and Distance
  • Trignometry – Identities
  • Trignometry – Introduction

Middle School Science

  • Acids, Bases And Salts
  • Air and Its Constituents
  • Basic Biology
  • Body Movements
  • Carbon and Its Compounds
  • Cell – Structure And Functions
  • Changes Around Us
  • Chemical Effects Of Electric Current
  • Chemistry in Your Life
  • Coal And Petroleum
  • Combustion And Flame
  • Components Of Food
  • Conservation Of Plants And Animals
  • Crop Production And Management
  • Electric Current And Its Effects
  • Electricity And Circuits
  • Elements and Compounds
  • Fibre To Fabric
  • Food production and management
  • Force And Pressure
  • Forests: Our Lifeline
  • Friction
  • Fun With Magnets
  • Garbage In, Garbage Out
  • Getting To Know Plants
  • Health and Hygiene
  • Heat
  • Hydrogen
  • Life Processes: Nutrition in Animals and Plants
  • Light, Shadows And Reflections
  • Materials: Metals And Non-Metals
  • Matter and Its States
  • Metals and Non-metals
  • Micro Organisms: Friend And Foe
  • Motion And Measurement Of Distances
  • Motion And Time
  • Nutrition In Animals
  • Nutrition In Plants
  • Organization in Living Things
  • Our Environment
  • Physical And Chemical Changes
  • Pollution and conservation
  • Pollution Of Air And Water
  • Reaching The Age Of Adolescence
  • Reproduction In Animals
  • Reproduction In Plants
  • Respiration In Organisms
  • Rocks and Minerals
  • Separation Of Substances
  • Simple Machines
  • Soil
  • Some Natural Phenomena
  • Sorting Materials Into Groups
  • Sound
  • Stars And The Solar System
  • Structure of Atom
  • Synthetic Fibers And Plastics
  • The Living Organisms And Their Surroundings
  • Transfer of Heat
  • Transformation of Substances
  • Transportation In Animals And Plants
  • Universe
  • Waste-water Story
  • Water: A Precious Resource
  • Weather, Climate And Adaptations Of Animals To Climate
  • Winds, Storms And Cyclones

Middle School Math

  • Addition
  • Area and Its Boundary
  • Boxes and Sketches
  • Data Handling
  • Fun With Numbers
  • Heavy and Light
  • How Many
  • Long And Short
  • Mapping
  • Measurement
  • Money
  • Multiplication and Factors
  • Multiply and Divide
  • Numbers
  • Parts and Wholes
  • Pattern Recognition
  • Patterns
  • Play With Patterns
  • Rupees And Paise
  • Shapes And Angles
  • Shapes And Designs
  • Shapes and Space
  • Similarity
  • Smart Charts
  • Squares
  • Subtraction
  • Tables And Shares
  • Tenths and Hundredths
  • Time
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