# Prime Time

## Overview

In this chapter, students explore the ideas of factors, multiples, prime numbers, co-primes, prime factorisation, and divisibility tests. The chapter is designed with engaging games, puzzles, and activities to develop logical reasoning and number sense.

## Key Topics Covered

### 1. The Idli-Vada Game (Common Multiples)

* Numbers which are multiples of 3: say "idli"
* Numbers which are multiples of 5: say "vada"
* Numbers which are multiples of both 3 and 5: say "idli-vada"
* **Key Concept**: Common multiples and Least Common Multiple (LCM)

### 2. Jump Jackpot (Common Factors)

* Game involves jumping in fixed-size steps to reach a number.
* Factors are numbers that divide a given number exactly.
* **Key Concept**: Finding all factors; identifying common factors.

### 3. Prime and Composite Numbers

* **Prime Numbers**: Only two factors (1 and itself), e.g., 2, 3, 5, 7, 11
* **Composite Numbers**: More than two factors, e.g., 4, 6, 8, 9
* **Special Case**: 1 is neither prime nor composite.
* **Sieve of Eratosthenes**: A method to find all prime numbers up to 100

### 4. Co-prime Numbers

* Two numbers with no common factor other than 1 are co-prime.
* Example: 4 and 9 are co-prime; 15 and 39 are not.
* **Use in Games and Art**: Identifying co-prime pairs leads to safe treasure hiding or complete thread art.

### 5. Prime Factorisation

* Breaking a number into product of prime numbers.
* Unique prime factorisation (order doesn’t matter).
* Used to:

* Check if numbers are co-prime
* Check if one number is divisible by another

### 6. Divisibility Tests

* **Divisible by 10**: Number ends in 0
* **Divisible by 5**: Number ends in 0 or 5
* **Divisible by 2**: Number ends in 0, 2, 4, 6, or 8
* **Divisible by 4**: Last 2 digits form a number divisible by 4
* **Divisible by 8**: Last 3 digits form a number divisible by 8

### 7. Fun With Numbers

* Puzzles based on square numbers, prime properties, and special patterns.
* Identify twin primes, palindrome numbers divisible by 4, and products of prime numbers.

## New Terms and Definitions

| Term | Definition |
| --------------------- | ---------------------------------------------------------------------------- |
| Factor | A number that divides another number exactly |
| Multiple | A number that is the result of multiplying a number by an integer |
| Prime Number | A number with only two factors: 1 and itself |
| Composite Number | A number with more than two factors |
| Co-prime Numbers | Two numbers with no common factor except 1 |
| Prime Factorisation | Expressing a number as a product of prime numbers |
| Divisible | A number is divisible by another if it can be divided exactly (no remainder) |
| Sieve of Eratosthenes | A method to find all prime numbers up to a certain limit by elimination |

## Practice Questions

### Easy (3)

1. What are the factors of 12?
**Answer**: 1, 2, 3, 4, 6, 12

2. Is 15 a prime or composite number?
**Answer**: Composite (factors are 1, 3, 5, 15)

3. What are the first three multiples of 4?
**Answer**: 4, 8, 12

### Medium (2)

4. Find the prime factorisation of 36.
**Answer**: 2 × 2 × 3 × 3

5. Are 14 and 25 co-prime?
**Answer**: Yes (no common factors except 1)

### Difficult (3)

6. Is 1008 divisible by 8? Explain.
**Answer**: Yes. Last 3 digits are 008, which is divisible by 8.

7. Find all the prime numbers between 20 and 30.
**Answer**: 23, 29

8. Check if 225 is divisible by 5 and 10.
**Answer**: Yes, divisible by 5 (ends in 5); No, not divisible by 10 (does not end in 0)

### Very Difficult (2)

9. Find the smallest number that is divisible by all numbers from 1 to 10.
**Answer**: 2520

10. Write a 4-digit palindrome that is divisible by 4.
**Answer**: 2442 (Last 2 digits 42 are divisible by 4)