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
-
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. -
Question: Is 231 divisible by 3 and 11?
Solution: Yes, 231 is divisible by both 3 and 11. -
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.