Meaning of a factor and a common factor for JSS 1

Class: JSS 1
Term: First Term
Week: 5
Age: 12 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: NUMBER NUMERATION
Focal competence: Calculating the HCF of two or more whole numbers
Key competencies/values: Collaboration; ICT and Digital Competencies
Skills:

• Calculating of LCM and HCF

Previous Lesson: Meaning of Lowest Common Multiple (LCM) and Multiple of whole numbers
Topic: Meaning of a Factor and a Common Factor
Subject Matter: Meaning of a factor, Meaning of a common factor, Meaning of Highest Common Factor (HCF), Factors and common factors of whole numbers

Specific Objectives

By the end of the lesson, pupils/students should be able to:

Cognitive Domain

• define a factor;
• define a common factor;
• define Highest Common Factor (HCF);
• identify factors and common factors of whole numbers.

Affective Domain

• collaborate with peers to identify factors and common factors.

Psychomotor Domain

• list factors and common factors for given whole numbers.

Reference Materials

The following resources were used in planning this lesson:

• 2025 Revised 9 Years Basic Education Curriculum
• Relevant State Unified Scheme of Work
• Mathematics Open references
• A suitable JSS 1 Mathematics textbook
• The HeadTeacher Scheme of work

Instructional Materials

The teacher will teach this lesson with the aid of:

• Whiteboard and markers
• Charts showing multiplication tables
• Number cards
• Interactive HCF calculator (for demonstration)
• Maths Is Fun website (for reference)
• Coolmath HCF lesson and practices (for reference)
• LCM and HCF by CK-12 (for reference)

Rationale for the Lesson

Understanding factors and common factors is foundational to many areas of mathematics, including fractions, algebra, and number theory. This lesson provides students with the basic concepts needed to simplify expressions and solve problems involving divisibility. It builds a strong base for future topics like Lowest Common Multiple (LCM) and algebraic factorization.

Prerequisite/Previous Knowledge

Students should have a good understanding of basic multiplication and division operations involving whole numbers.

Lesson Content/Board Summary

Meaning of a Factor and a Common Factor

Meaning of a Factor

A factor of a whole number is any whole number that divides it exactly without leaving a remainder. In other words, when you multiply two whole numbers to get a product, both numbers are factors of that product.

For example, in (3 times 4 = 12), 3 and 4 are factors of 12.

Exact Division and Factor Pairs

When a number divides another number exactly, it means the remainder is zero. Factors often come in pairs, called factor pairs.

1. To find factor pairs, think of two numbers that multiply to give the original number.
2. For example, for 12, the factor pairs are:
1. (1 times 12 = 12)
2. (2 times 6 = 12)
3. (3 times 4 = 12)

Listing Factors of Whole Numbers

To list all factors of a number, start from 1 and test each whole number up to the square root of the number. If a number divides exactly, then both the divisor and the quotient are factors.

1. Example 1: List the factors of 18.
1. (1 times 18 = 18)
2. (2 times 9 = 18)
3. (3 times 6 = 18)
4. 4 does not divide 18 exactly.
5. 5 does not divide 18 exactly.
6. 6 is already listed.

The factors of 18 are 1, 2, 3, 6, 9, 18.

2. Example 2: List the factors of 24.
1. (1 times 24 = 24)
2. (2 times 12 = 24)
3. (3 times 8 = 24)
4. (4 times 6 = 24)

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.

Meaning of a Common Factor

A common factor of two or more whole numbers is a factor that is shared by all of those numbers. It is a number that divides each of the given numbers exactly.

Identifying Common Factors

To identify common factors of two or more numbers:

1. List all the factors for each number.
2. Identify the factors that appear in all the lists.

Example: Find the common factors of 18 and 24.

1. Factors of 18: 1, 2, 3, 6, 9, 18
2. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
3. The numbers that appear in both lists are 1, 2, 3, 6.

Therefore, the common factors of 18 and 24 are 1, 2, 3, 6.

Meaning of Highest Common Factor (HCF)

The Highest Common Factor (HCF) of two or more whole numbers is the largest number among their common factors. It is also known as the Greatest Common Divisor (GCD).

Example: From the common factors of 18 and 24 (which are 1, 2, 3, 6), the highest number is 6.

Therefore, the HCF of 18 and 24 is 6.

Teaching Methods/Instructional Techniques

Discussion, Explanation, Question and Answer, Guided Practice, Individual Practice

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Recalling/Engaging

Teacher’s Activity: The teacher greets the students and reviews basic multiplication and division facts. The teacher asks, “What does it mean for one number to divide another number exactly?” and “Can you give an example of two numbers that multiply to give 10?”

Pupils’ Activity: Students respond to the questions, recalling previous knowledge of multiplication and exact division.

Learning Point: Prior knowledge recall

Step 2: Meaning of a Factor

Time: 8 minutes

Teaching Skill: Explaining/Defining

Teacher’s Activity: The teacher introduces the term “factor” and explains its meaning using simple examples like 12. “If 3 divides 12 exactly, then 3 is a factor of 12. If 4 divides 12 exactly, then 4 is a factor of 12.” The teacher writes the definition on the board.

Pupils’ Activity: Students listen attentively, ask questions for clarity, and copy the definition of a factor.

Learning Point: Factor definition

Step 3: Exact Division and Factor Pairs

Time: 7 minutes

Teaching Skill: Demonstrating/Illustrating

Teacher’s Activity: The teacher explains the concept of exact division (remainder is zero) and introduces factor pairs. Using the number 12, the teacher demonstrates how (1 times 12), (2 times 6), and (3 times 4) are factor pairs, and how each number in the pair is a factor.

Pupils’ Activity: Students observe the examples and participate in identifying factor pairs for other small numbers like 10 or 15.

Learning Point: Exact division concept

Step 4: Listing Factors of Whole Numbers

Time: 8 minutes

Teaching Skill: Guiding/Practicing

Teacher’s Activity: The teacher guides students through the process of listing all factors of a given whole number, such as 18 and 24, as shown in the Board Summary. The teacher encourages students to work systematically.

Pupils’ Activity: Students follow along, list factors in their notebooks, and attempt to list factors for other numbers like 20 or 30 under the teacher’s guidance.

Learning Point: Listing factors

Step 5: Meaning of a Common Factor

Time: 5 minutes

Teaching Skill: Explaining/Defining

Teacher’s Activity: The teacher introduces the term “common factor” as a factor shared by two or more numbers. The teacher writes the definition on the board and prepares to use the previous examples (18 and 24) to illustrate.

Pupils’ Activity: Students listen to the explanation and copy the definition of a common factor.

Learning Point: Common factor definition

Step 6: Identifying Common Factors and HCF

Time: 5 minutes

Teaching Skill: Demonstrating/Applying

Teacher’s Activity: Using the lists of factors for 18 and 24, the teacher demonstrates how to identify the common factors (1, 2, 3, 6). The teacher then defines the Highest Common Factor (HCF) as the largest among these common factors, which is 6.

Pupils’ Activity: Students identify the common factors and the HCF from the given lists and ask questions for clarification.

Learning Point: Identifying common factors

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. What is a factor of a number?
2. List all factors of 15.
3. What is a common factor?
4. Find the common factors of 12 and 18.
5. What does HCF stand for?

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Lesson understanding

Step 8: Note-Taking

Time: 4 minutes

Teaching Skill: Guided Writing

Teacher’s Activity: The teacher guides pupils/students to copy the essential Board Summary notes on factors, common factors, and HCF into their notebooks.

Pupils’ Activity: Pupils/students copy the notes carefully into their notebooks.

Learning Point: Notes copying

Step 9: Conclusion

Time: 3 minutes

Teaching Skill: Summarising/Consolidating

Teacher’s Activity: The teacher briefly recaps the definitions of factor, common factor, and HCF, emphasizing their importance in mathematics. The teacher encourages students to practice listing factors at home.

Pupils’ Activity: Students listen and ask any final questions.

Learning Point: Key concepts consolidation

Continuous Assessment/Further Study

Type: Homework

Instruction: Answer the following questions in your notebook:

1. Define a factor in your own words.
2. List all the factors of 20.
3. List all the factors of 30.
4. Identify the common factors of 20 and 30.
5. What is the HCF of 20 and 30?

Lesson Keywords

• Factor – A number that divides another number exactly without a remainder.
• Exact Division – Division that results in a remainder of zero.
• Factor Pair – Two numbers that multiply together to give a specific product.
• Common Factor – A factor shared by two or more numbers.
• Highest Common Factor (HCF) – The largest number among the common factors of two or more numbers.

Differentiation

For weaker learners, provide additional practice with simpler numbers and use multiplication tables as a direct aid. For faster learners, challenge them to find factors for larger numbers or to explore the concept of prime factors in relation to common factors, preparing them for the next lesson on HCF calculation methods.

Suggested Lesson Videos

For further understanding, search on YouTube for: factors and common factors jss1 mathematics

Teacher Guide for Using This Lesson Plan

Before the lesson, ensure you have charts of multiplication tables ready and clear examples prepared for factors and common factors. Begin by activating students’ prior knowledge of multiplication and division to build a bridge to the new concepts. Follow the instructional procedures step-by-step, providing clear explanations and guided practice for each new term. Pay close attention to students’ understanding of exact division as it is central to identifying factors. Encourage collaboration during factor listing exercises. During the note-taking stage (Step 8), ensure students copy the Board Summary accurately. For evaluation, use questions directly aligned with the performance objectives to check for understanding. Provide constructive feedback and encourage further practice at home to reinforce learning.