Grade 4
  1. Numbers and Place Value  1.1. Understanding Place Value  1.2. Reading and Writing Large Numbers  1.3. Comparing and Ordering Numbers  1.4. Rounding Numbers  1.5. Understanding Odd and Even Numbers  1.6. Number Patterns and Sequences
  2. Addition and Subtraction  2.1. Addition of Large Numbers  2.2. Subtraction of Large Numbers  2.3. Estimation in Addition and Subtraction  2.4. Word Problems on Addition and Subtraction
  3. Multiplication and Division  3.1. Understanding Multiplication  3.2. Multiplying Multi-Digit Numbers  3.3. Understanding Division  3.4. Dividing Multi-Digit Numbers  3.5. Multiplication and Division Facts  3.6. Word Problems on Multiplication and Division
  4. Factors and Multiples  4.1. Understanding Factors  4.2. Finding Common Factors  4.3. Understanding Multiples  4.4. Finding Common Multiples  4.5. Prime and Composite Numbers  4.6. Prime Factorization  4.7. Greatest Common Factor  4.8. Least Common Multiple
  5. Fractions  5.1. Understanding Fractions  5.2. Equivalent Fractions  5.3. Simplifying Fractions  5.4. Comparing and Ordering Fractions  5.5. Addition of Fractions  5.6. Subtraction of Fractions  5.7. Mixed Numbers and Improper Fractions  5.8. Converting Mixed Numbers to Improper Fractions  5.9. Word Problems on Fractions
  6. Decimals  6.1. Understanding Decimals  6.2. Reading and Writing Decimals  6.3. Comparing and Ordering Decimals  6.4. Rounding Decimals  6.5. Addition of Decimals  6.6. Subtraction of Decimals  6.7. Converting Decimals to Fractions  6.8. Converting Fractions to Decimals  6.9. Word Problems on Decimals
  7. Measurement  7.1. Length  7.1.1. Units of Length  7.1.2. Converting Units of Length  7.1.3. Perimeter  7.1.4. Area  7.1.5. Word Problems on Length  7.2. Weight  7.2.1. Units of Weight  7.2.2. Converting Units of Weight  7.2.3. Word Problems on Weight  7.3. Volume and Capacity  7.3.1. Units of Volume  7.3.2. Converting Units of Volume  7.3.3. Estimating Volume and Capacity  7.3.4. Word Problems on Volume and Capacity  7.4. Time  7.4.1. Reading Time  7.4.2. Units of Time  7.4.3. Converting Units of Time  7.4.4. Calculating Elapsed Time  7.4.5. Word Problems on Time
  8. Geometry  8.1. Properties of Shapes  8.1.1. Types of Angles  8.1.2. Types of Triangles  8.1.4. Symmetry  8.1.5. Lines of Symmetry  8.2. Perimeter and Area  8.2.1. Perimeter of Rectangles  8.2.2. Perimeter of Other Shapes  8.2.3. Area of Rectangles  8.2.4. Area of Other Shapes  8.2.5. Area of Irregular Shapes  8.3. Coordinate Geometry  8.3.1. Understanding Coordinates  8.3.2. Plotting Points on a Grid  8.3.3. Identifying Shapes on a Grid
  9. Data and Graphs  9.1. Types of Data  9.2. Organizing Data  9.3. Reading Bar Graphs  9.4. Drawing Bar Graphs  9.5. Line Plots  9.7. Reading and Interpreting Line Graphs  9.8. Word Problems on Graphs
  10. Money  10.1. Understanding Money  10.2. Addition and Subtraction with Money  10.3. Making Change  10.4. Multiplying and Dividing Money  10.5. Word Problems on Money

Grade 4 ↓


Factors and Multiples


In this lesson, we will dive deep into the world of factors and multiples. These are fundamental concepts in mathematics, often introduced in early classes. Understanding factors and multiples is essential because they are important for understanding more advanced topics in mathematics, such as fractions. They form the basis for algebra and number theory. This guide will tell you what factors and multiples are, how to identify them, and how they are used in simple arithmetic problems.

Understanding the factors

A factor is a number that divides another number without a remainder. For example, if you wanted to find the factors of the number 12, you would look at all the numbers that divide 12 evenly:

  • 1 (because 12 ÷ 1 = 12),
  • 2 (because 12 ÷ 2 = 6),
  • 3 (because 12 ÷ 3 = 4),
  • 4 (because 12 ÷ 4 = 3),
  • 6 (because 12 ÷ 6 = 2),
  • 12 (because 12 ÷ 12 = 1).

The factors of 12 are 1, 2, 3, 4, 6, and 12. These are all numbers that can be multiplied together to get 12:

1 × 12 = 12 2 × 6 = 12 3 × 4 = 12

Visual example

Let's represent this visually using points:

<svg width="100" height="100"> <circle cx="10" cy="10" r="5" fill="blue" /> <circle cx="30" cy="10" r="5" fill="blue" /> <circle cx="50" cy="10" r="5" fill="blue" /> <circle cx="70" cy="10" r="5" fill="blue" /> <circle cx="10" cy="30" r="5" fill="blue" /> <circle cx="30" cy="30" r="5" fill="blue" /> <circle cx="10" cy="50" r="5" fill="blue" /> <circle cx="30" cy="50" r="5" fill="blue" /> <circle cx="10" cy="70" r="5" fill="blue" /> </svg>

This grid shows 12 points arranged in groups. Different rows represent different factors.

What are multiples?

The multiple of a number is the product of that number and an integer. In simple terms, it is like skip counting. For example, if you want to find the multiples of 3, you multiply 3 by 1, 2, 3, and so on:

  • 3 × 1 = 3,
  • 3 × 2 = 6,
  • 3 × 3 = 9,
  • 3 × 4 = 12,
  • 3 × 5 = 15, etc.

This means that 3, 6, 9, 12, and 15 are multiples of 3. This can be represented visually as:

<svg width="100" height="20"> <circle cx="10" cy="10" r="5" fill="red" /> <circle cx="30" cy="10" r="5" fill="red" /> <circle cx="50" cy="10" r="5" fill="red" /> </svg>

The circles represent some multiples of 3.

Difference between factor and multiple

It is important to understand that factors are numbers that you multiply together to get another number, while multiples are numbers that you get by multiplying a number by another number. Let's understand this relationship more with some examples:

The factors of 6 are the numbers that when multiplied can give the number 6. These include 1, 2, 3, and 6, because:

1 × 6 = 6 2 × 3 = 6

Multiples of 6 are the numbers you get when you add 6. These include:

6, 12, 18, 24, 30, etc.

Checking some special numbers

Prime numbers

Prime numbers are a special type of numbers that have only two factors: 1 and the number itself. For example, the number 7 is a prime number because the only two factors of 7 are 1 and 7.

Composite numbers

Composite numbers are numbers that have more than two factors. For example, the number 12 is a composite number because it has six factors: 1, 2, 3, 4, 6, and 12.

Finding the greatest common factor (GCF)

The greatest common factor (or GCF) of two numbers is the largest number that is a factor of both numbers. For example, the factors of 8 are 1, 2, 4, and 8. The factors of 12 are 1, 2, 3, 4, 6, and 12. The common factors between them are 1, 2, and 4. The largest of these is 4.

Finding the least common multiple (LCM)

The least common multiple (or LCM) of two numbers is the smallest number that is a multiple of both numbers. Taking the numbers 3 and 4, the multiples of 3 are 3, 6, 9, 12, 15, and so on. Multiples of 4 are 4, 8, 12, 16, etc. The smallest multiple they have in common is 12.

Practice problems

Finding factors

Try to find the factors of the following numbers:

  • The number 15. The factors are: 1, 3, 5, 15.
  • The number 20. The factors are: 1, 2, 4, 5, 10, 20.

Finding multiples

Let's practice listing the first few multiples of these numbers:

  • The number 5. The multiples are: 5, 10, 15, 20, 25, etc.
  • The number 7. Its multiples are: 7, 14, 21, 28, 35, etc.

Short

In short, factors are numbers that you can multiply together to get another number. Multiples are what you get when you keep adding a number to itself. Remember, understanding factors and multiples is very important because they form the key building blocks for many other mathematical concepts.

Conclusion

Factors and multiples are integral parts of elementary mathematics. They help in many ways, including simplifying fractions, working with algebraic expressions, and understanding relationships between numbers. Regular practice and the use of visual tools help master these concepts. With such an understanding, you will be well prepared for the challenges in higher mathematics.


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