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Mathematics Class 8 - Playing With-Numbers Notes

Comprehensive study notes for Class 8 - Playing With-Numbers olympiad preparation

Playing with Numbers

Welcome to the chapter on Playing with Numbers for Class 8. In this chapter, you will explore interesting properties of numbers, learn about divisibility, factors, multiples, prime and composite numbers, and solve puzzles and problems using these concepts. By the end of this chapter, you will be able to use number properties to solve challenging math problems!

Introduction

Numbers are everywhere! In this chapter, you will learn how to play with numbers using their properties, patterns, and rules. Understanding numbers helps you solve puzzles and makes math fun.

Divisibility Rules

Divisibility rules help us quickly check if one number can be divided by another without a remainder.

  • 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, 8).
  • 3: If the sum of the digits is divisible by 3.
  • 4: If the last two digits form a number divisible by 4.
  • 5: If the last digit is 0 or 5.
  • 6: If the number is divisible by both 2 and 3.
  • 9: If the sum of the digits is divisible by 9.
  • 10: If the last digit is 0.

Factors and Multiples

  • Factor: A number that divides another number exactly.
  • Multiple: The result of multiplying a number by an integer.
  • Example: Factors of 12 are 1, 2, 3, 4, 6, 12. Multiples of 3 are 3, 6, 9, 12, ...

Prime and Composite Numbers

  • Prime Number: Has only two factors: 1 and itself. Example: 2, 3, 5, 7, 11
  • Composite Number: Has more than two factors. Example: 4, 6, 8, 9, 12

Perfect Numbers and Co-primes

  • Perfect Number: A number whose factors (excluding itself) add up to the number. Example: 6 (1+2+3=6)
  • Co-primes: Two numbers with no common factors except 1. Example: 8 and 15

Playing with Digits

You can form new numbers by rearranging digits, check for palindromes, and solve puzzles using digit properties.

  • Palindrome: A number that reads the same forwards and backwards. Example: 121, 1331
  • Reversing digits: 123 becomes 321

Number Puzzles and Patterns

Numbers can form interesting patterns. Try to spot them and solve puzzles!

  • Find the next number in a sequence.
  • Magic squares and Sudoku use number patterns.

Fun Activity: Number Magic!

Pick any three-digit number. Reverse its digits and subtract the smaller from the bigger. Reverse the result and add. You will get 1089!

Summary

  • Divisibility rules help check if numbers can be divided.
  • Factors and multiples are important in math.
  • Prime numbers have only two factors; composite numbers have more.
  • Playing with digits and patterns makes math fun!

Practice Questions

  1. List all factors of 24.
  2. Is 17 a prime or composite number?
  3. Find the next number: 2, 4, 8, 16, ___
  4. Which numbers between 10 and 20 are divisible by 3?
  5. What is a palindrome number? Give an example.

Challenge Yourself

  • Find two co-prime numbers between 20 and 30.
  • Write a four-digit palindrome number.

Did You Know?

  • Zero is neither prime nor composite!
  • The largest known prime number has millions of digits!

Glossary

  • Divisibility: Ability to be divided by another number without remainder.
  • Factor: A number that divides another exactly.
  • Multiple: The result of multiplying a number.
  • Prime Number: Has only two factors: 1 and itself.
  • Composite Number: Has more than two factors.
  • Palindrome: Number that reads the same forwards and backwards.

Answers to Practice Questions

  1. 1, 2, 3, 4, 6, 8, 12, 24
  2. Prime
  3. 32
  4. 12, 15, 18
  5. A number that reads the same forwards and backwards. Example: 1221

Explore and play with numbers to discover their magic!

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