Mathematics Notes for Class 6 Playing With-Numbers

Playing with Numbers

Welcome to the chapter on Playing with Numbers for Class 6. In this chapter, you will learn about numbers, their properties, and how to use them in different ways. By the end of this chapter, you will be able to solve problems using factors, multiples, prime and composite numbers, and understand divisibility rules!

Introduction

Numbers are everywhere! We use them to count, measure, and solve problems. In this chapter, you will explore interesting facts about numbers and learn new ways to work with them.

Factors and Multiples

Factors are numbers that divide another number exactly.
Multiples are numbers you get by multiplying a number by 1, 2, 3, and so on.

Example: Factors of 12 are 1, 2, 3, 4, 6, 12.
Example: Multiples of 5 are 5, 10, 15, 20, ...

Prime and Composite Numbers

Prime numbers have only two factors: 1 and itself.
Composite numbers have more than two factors.

Example: 7 is prime (factors: 1, 7)
Example: 8 is composite (factors: 1, 2, 4, 8)

Divisibility Rules

Divisibility rules help us check if a number can be divided by another number without doing actual division.

A number is divisible by 2 if its last digit is even.
A number is divisible by 3 if the sum of its digits is divisible by 3.
A number is divisible by 5 if it ends in 0 or 5.

Highest Common Factor (HCF) and Lowest Common Multiple (LCM)

HCF is the greatest number that divides two or more numbers exactly.
LCM is the smallest number that is a multiple of two or more numbers.

Example: HCF of 12 and 18 is 6.
Example: LCM of 4 and 6 is 12.

Playing with Patterns

Numbers can form patterns. Look for patterns in sequences and try to find the rule!

Example: 2, 4, 6, 8, ... (Pattern: add 2 each time)
Example: 1, 4, 9, 16, ... (Pattern: square numbers)

Fun Activity: Number Hunt!

Pick a number and find all its factors and multiples. Try to find prime numbers between 1 and 50!

Summary

Numbers have many interesting properties.
Learn about factors, multiples, prime and composite numbers.
Use divisibility rules, HCF, and LCM to solve problems.

Practice Questions

List all factors of 24.
Write the first five multiples of 7.
Is 17 a prime or composite number?
Find the HCF of 20 and 30.
Find the LCM of 6 and 8.
Is 45 divisible by 3?

Challenge Yourself

Find all prime numbers between 10 and 30.
Make a pattern using numbers and explain the rule.

Did You Know?

Zero is not a prime or composite number.
The number 2 is the only even prime number.

Glossary

Factor: A number that divides another number exactly.
Multiple: A number you get by multiplying.
Prime Number: Has only two factors: 1 and itself.
Composite Number: Has more than two factors.
Divisibility: Ability to be divided by another number without remainder.
HCF: Highest Common Factor.
LCM: Lowest Common Multiple.

Answers to Practice Questions

1, 2, 3, 4, 6, 8, 12, 24
7, 14, 21, 28, 35
Prime
10
24
Yes (4 + 5 = 9, which is divisible by 3)

Numbers are fun! Keep exploring and playing with numbers every day!

Mathematics Class 6 - Playing With-Numbers Notes