Chapter: 3 : Introduction
Playing with Numbers
Welcome to Chapter 3! In this chapter, we’ll explore how numbers behave, how they connect with each other, and discover fun patterns that help us solve problems quickly.
What have we learned so far?
We’ve played with multiples, factors, and divisors. Here’s a quick recap:
1. About Factors & Multiples:
- A factor divides a number exactly (no remainder).
- Every number is a factor of itself. 1 is a factor of every number.
- All factors are ≤ the number.
- Every number is a multiple of each of its factors.
- Multiples are ≥ the number. And yes—every number is a multiple of itself!
2. Prime & Composite Numbers:
- Prime numbers have only two factors: 1 and the number itself.
Example: 2, 3, 5, 7…
- Composite numbers have more than two factors.
Example: 4, 6, 8, 9…
- 1 is neither prime nor composite.
- 2 is the smallest—and only even—prime number!
- Two numbers with only 1 as a common factor are called co-prime.
3. Divisibility Rules (Superpowers!):
- 🔢 2, 5, 10 → Check the last digit.
- ➕ 3, 9 → Add all digits. If the sum is divisible, so is the number!
- 🧮 4 → Look at the last 2 digits.
- 🧮 8 → Look at the last 3 digits.
- ⚖️ 11 → Subtract sum of digits in even places from sum in odd places. If result is 0 or divisible by 11 → yes!
4. Cool Number Tricks:
- If two numbers are divisible by a number, then their sum and difference are also divisible by it!
- If a number is divisible by two co-prime numbers, it’s also divisible by their product.
5. HCF & LCM:
- HCF (Highest Common Factor): The biggest number that divides two or more numbers.
- LCM (Lowest Common Multiple): The smallest number that is a multiple of two or more numbers.
Remember: Numbers aren’t just for counting—they tell stories, hide patterns, and follow rules. In this chapter, you’ll become a Number Detective! 🔍