Factors and Multiples

Grade 7 Math - Factors and Multiples

Lesson Objectives

Define and identify factors and multiples of numbers.
Understand the difference between factors and multiples.
Identify prime numbers and their role in mathematics.

Lesson Introduction

Understanding factors and multiples helps us work with numbers efficiently. From calculating time schedules to solving math problems, these concepts appear everywhere. In this lesson, you will learn how to identify them and explore the idea of prime numbers.

Core Lesson Content

Definition of Factor: A factor of a number divides it exactly without remainder.

Example: Factors of 12 are: $1, 2, 3, 4, 6, 12$

Definition of Multiple: A multiple of a number is the result of multiplying it by whole numbers.

Example: First five multiples of 4: $4, 8, 12, 16, 20$

Definition of Prime Number: A prime number has exactly two factors — 1 and itself.

Example: $2, 3, 5, 7, 11, 13, 17$

Worked Examples

Example 1: List all the factors of 18.

1, 2, 3, 6, 9, 18

Explanation: Each number above divides 18 exactly.

Example 2: Write the first five multiples of 6.

6, 12, 18, 24, 30

Explanation: Multiply 6 by 1 to 5.

Example 3: Is 19 a prime number?

\text{Factors of 19: 1 and 19} \Rightarrow \text{Prime}

Explanation: Only divisible by 1 and itself.

Example 4: Find all the factors of 20.

1, 2, 4, 5, 10, 20

Explanation: All these divide 20 exactly.

Example 5: List the multiples of 3 between 10 and 30.

12, 15, 18, 21, 24, 27, 30

Explanation: All are divisible by 3 within the range.

Example 6: Is 1 a prime number?

\text{Only one factor (1)} \Rightarrow \text{Not Prime}

Explanation: A prime number must have exactly two distinct factors.

Example 7: Write first 4 multiples of 7.

7, 14, 21, 28

Explanation: Multiply 7 by 1 to 4.

Example 8: What are the prime numbers between 1 and 10?

2, 3, 5, 7

Explanation: Each has only two factors: 1 and itself.

Example 9: Find the factors of 15.

1, 3, 5, 15

Explanation: All divide 15 without remainder.

Example 10: List all prime numbers less than 20.

2, 3, 5, 7, 11, 13, 17, 19

Explanation: All these numbers are only divisible by 1 and themselves.

Exercises

Find all the factors of 24.
[NABTEC] List the first six multiples of 9. [Past Question]
Is 29 a prime number?
Which numbers less than 30 are prime?
[WAEC] List all the factors of 36. [Past Question]
[NECO] Write all the multiples of 5 from 1 to 50. [Past Question]
Find the prime numbers between 10 and 30.
[JAMB] Write the first 5 multiples of 11. [Past Question]
Find the factors of 45.
Is 51 a prime number?

Conclusion/Recap

Today, you learned to identify factors, multiples, and prime numbers. These concepts form the building blocks of higher mathematics. In the next lesson, we’ll explore LCM and HCF using these concepts.