Playing with Numbers

This chapter explores interesting properties and patterns of numbers, including divisibility, factors, multiples, and number puzzles. It helps students develop logical thinking and problem-solving skills by working with numbers in creative ways.

1. Numbers and Their Properties

• Understanding natural numbers, whole numbers, and integers.
• Prime and composite numbers.
• Even and odd numbers.
• Perfect numbers and co-prime numbers.

2. Factors and Multiples

• Finding factors and multiples of a given number.
• Highest Common Factor (HCF) and Lowest Common Multiple (LCM).
• Prime factorization.

3. Divisibility Tests

• Rules for divisibility by 2, 3, 4, 5, 6, 8, 9, 10, and 11.
• Applying divisibility tests to solve problems quickly.

4. Number Puzzles and Patterns

• Magic squares and number grids.
• Finding missing numbers in patterns.
• Exploring interesting number tricks.

5. Letters for Digits

• Solving puzzles where letters stand for digits (cryptarithms).
• Examples: SEND + MORE = MONEY.

6. Word Problems

1. Question: Find the HCF and LCM of 18 and 24.
   Solution: Factors of 18: 1, 2, 3, 6, 9, 18; Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
   HCF = 6, LCM = 72.
2. Question: Is 231 divisible by 3 and 11?
   Solution: Yes, 231 is divisible by both 3 and 11.
3. Question: Fill in the blank: The smallest number divisible by 4, 6, and 8 is ____.
   Solution: 24.

7. Practice Exercises

• List all factors of 36.
• Find the LCM of 12, 15, and 20.
• Which of the following numbers are divisible by 9: 234, 567, 891?
• Solve the puzzle: If A + B = 10 and both A and B are single-digit numbers, what are the possible values of A and B?

8. Summary

• Numbers have interesting properties and patterns.
• Divisibility rules help in quick calculations.
• Factors and multiples are useful in solving many problems.
• Number puzzles develop logical and analytical skills.