Factors and Multiples for Class 5 [+12 Worksheets]

This is a comprehensive lesson plan for teaching factors and multiples to grade 5 students. The lesson is designed to make the concepts easy and engage students with activities like real-life examples, quizzes, practice questions and worksheets.

Teachers can use this guide as a reference for delivering the concepts to students and engaging them in the classroom with the various questions and examples given on this page.

For parents, there are 12 downloadable practice worksheets that they can use for their kids.

In this article, you will learn:

• Understand the concepts of factors and multiples.

• Identify prime and composite numbers.

• Apply divisibility rules to check if a number is divisible by another.

• Find the Highest Common Factor (HCF) and Least Common Multiple (LCM).

• Use factors and multiples in real-life situations.

 

---

 

What Are Factors?

A factor of a number is a number that divides the given number completely without leaving any remainder.

For example:

• The factors of 12 are 1, 2, 3, 4, 6, and 12 because they divide 12 exactly.

• The factors of 16 are 1, 2, 4, 8, and 16.

Finding Factors of a Number

To find the factors of a number, follow these steps:

1. Start with 1 because 1 is a factor of every number.

2. Check if the number is divisible by 2, 3, 4, 5, etc., without leaving a remainder.

3. Continue until you reach the number itself.

Example: Factors of 24
24 = 1 × 24, 2 × 12, 3 × 8, 4 × 6
So, factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24.

 

---

 

What Are Multiples?

A multiple of a number is the result of multiplying that number by another whole number.

For example:

• Multiples of 5: 5, 10, 15, 20, 25, 30, …

• Multiples of 8: 8, 16, 24, 32, 40, 48, …

Finding Multiples of a Number

To find the first five multiples of a number:

• Multiply the number by 1, 2, 3, 4, and 5.

Example: Multiples of 7
7 × 1 = 7
7 × 2 = 14
7 × 3 = 21
7 × 4 = 28
7 × 5 = 35
So, the first five multiples of 7 are 7, 14, 21, 28, and 35.

 

---

 

Types of Numbers

 

 

---

 

Rules of Divisibility

 

---

 

Finding Factors & Multiples

Prime Factorization

Prime factorization is expressing a number as the product of its prime factors.

Example: Prime Factorization of 36

Method 1: Factor Tree

So, 36 = 2 × 2 × 3 × 3.

Method 2: Division Method

1. Divide 36 by the smallest prime number 2 → 36 ÷ 2 = 18

2. Divide 18 by 2 → 18 ÷ 2 = 9

3. Divide 9 by 3 → 9 ÷ 3 = 3

4. Divide 3 by 3 → 3 ÷ 3 = 1

So, 36 = 2 × 2 × 3 × 3.

 

---

 

Highest Common Factor (HCF)

The HCF of two numbers is the greatest number that divides both numbers completely.

Example: Find HCF of 36 and 54

Factors of 36 = {1, 2, 3, 4, 6, 9, 12, 18, 36}
Factors of 54 = {1, 2, 3, 6, 9, 18, 27, 54}
Common factors = {1, 2, 3, 6, 9, 18}
HCF = 18

 

---

 

Least Common Multiple (LCM)

The LCM of two numbers is the smallest number that is a multiple of both.

Example: Find LCM of 12 and 18

Multiples of 12 = {12, 24, 36, 48, 60, ...}
Multiples of 18 = {18, 36, 54, 72, ...}
LCM = 36

Using Prime Factorization:
12 = 2 × 2 × 3
18 = 2 × 3 × 3
LCM = 2 × 2 × 3 × 3 = 36

 

---

 

Real-Life Applications of Factors and Multiples

1. Arranging Chairs in a Hall

When setting up chairs for an event, organizers group them into equal rows to ensure proper arrangement.

For example:

• If there are 72 chairs, they can be arranged in rows of 6, 8, 9, or 12 (since these are factors of 72).

• If each row must have the same number of chairs, we use factors to determine the arrangement.

 

2. Distributing Sweets

When dividing sweets among children, we use factors to ensure each child gets an equal amount.

For example:

• If there are 36 chocolates to be distributed among 6, 9, or 12 children, we can divide them equally using factors.

• If there are 40 sweets and 5 children, each will get 8 sweets (since 40 ÷ 5 = 8).

 

3. Buying and Packing Fruits

Shops sell fruits in packs of specific numbers to make packaging easier.

For example:

• A vendor packs oranges in sets of 6 per bag. If a customer buys multiples of 6, such as 12, 18, or 24, they get full bags without leftovers.

• If you want enough oranges for 10 people, and each gets 3 oranges, you must buy a multiple of 3 (like 30, 60, or 90).

 

4️. Scheduling Traffic Lights

Traffic signals at different intersections follow specific cycles. They turn red, yellow, and green at set time intervals.

For example:

• If one signal changes every 30 seconds and another every 45 seconds, they will turn green together at the LCM of 30 and 45 = 90 seconds.

• This ensures smooth traffic flow using the Least Common Multiple (LCM).

 

5. Music Beats and Rhythm

Musicians use factors and multiples to set rhythms in songs.

For example:

• A song beat repeats every 4 seconds, while another repeats every 6 seconds. The beats match again at the LCM of 4 and 6 = 12 seconds.

• This ensures instruments stay in sync while playing music.

 

6. Synchronizing Clocks

Two clocks ring at different intervals, and we need to find when they ring together again.

For example:

• One clock rings every 20 minutes, and another rings every 30 minutes.

• To find when they ring together, we calculate LCM(20,30) = 60 minutes, meaning they will ring together every hour.

 

7. Sports and Games

Coaches often divide players into equal teams for games.

For example:

• If a coach has 56 players, they can be divided into teams of 7, 8, or 14 (since these are factors of 56).

• If they must form 4 equal teams, each team will have 56 ÷ 4 = 14 players.

 

---

 

Orchids' Resources

Click the button to download the ebook on factors and multiples

 

---

 

Things you have learned

• Factors and multiples are used in everyday life.
• Prime numbers have only two factors.
• HCF finds the greatest factor, while LCM finds the smallest multiple.