# 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 and Multiples

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.

#### Properties of Multiples

• 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 and Composite Numbers

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.

#### Some More Divisibility Rules

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:

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

#### Prime Factorisation

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.

#### Highest Common Factor

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.

#### Lowest Common Multiple

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.

#### Conclusion

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.

#### FAQs

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
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### High School Chemistry

• Acids, Bases and Salts
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• Plant Growth and Development
• Plant Kingdom
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• Pollution; Sources and its effects
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• The Fundamental Unit Of Life
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• 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
• Binomial Theorem
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### Middle School Science

• Acids, Bases And Salts
• Air and Its Constituents
• Basic Biology
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• Carbon and Its Compounds
• Cell – Structure And Functions
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• Coal And Petroleum
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• Getting To Know Plants
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• Matter and Its States
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• Reaching The Age Of Adolescence
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• 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

• 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