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 ↓


Understanding Factors


In the world of math, when we talk about factors, we are diving into an important foundation that helps us better understand numbers and their properties. Factors are essential building blocks in both multiplication and division. In this lesson, we will explore what factors are and how we can find them, including examples and visual aids to make these concepts clearer and more digestible. Let's continue on this journey to understand factors thoroughly.

What are the factors?

A factor is a number that divides another number evenly without leaving a remainder. In simple terms, if you can divide a number by another number and get a whole number in the end, then the number you divided by is a factor of the original number.

For example, when we say factors of 10, we're really asking, "What numbers can divide 10 exactly without leaving a remainder?" The answers are 1, 2, 5, and 10.

Mathematical representation

Factorization of a number n means:
Dividing n by a factor = whole number (i.e. no remainder)

Finding factors

To find the factors of a number, you need to check which numbers can divide it completely. Let's see the steps with an example:

Example

Find the factors of 12.

Let's list the numbers from 1 to 12 and see which number divides 12 exactly:

  • 12 ÷ 1 = 12 (whole number, so 1 is a factor)
  • 12 ÷ 2 = 6 (whole number, so 2 is a factor)
  • 12 ÷ 3 = 4 (whole number, so 3 is a factor)
  • 12 ÷ 4 = 3 (whole number, so 4 is a factor)
  • 12 ÷ 6 = 2 (whole number, so 6 is a factor)
  • 12 ÷ 12 = 1 (whole number, so 12 is a factor)

So the factors of 12 are 1, 2, 3, 4, 6, and 12.

Visualization of factors

Visual examples often help us understand concepts better. Let's imagine finding the factors of a number using rectangles:

factor of 12 1 2 3 4

Each rectangle represents a group of objects in whole numbers that are multiplied by 12. This visualization shows how groups of objects can represent factors.

Why are the factors important?

Factors play an important role in simplifying fractions, solving equations, and analyzing numbers into their component parts. Understanding factors allows us to do the following:

  • Simplify fractions: By dividing both the numerator and denominator by their common factors, we can bring fractions to their simplest form.
  • Factorization: Breaking a number into its prime factors helps us understand more about the nature of that number. This is especially helpful in algebra.
  • Division and multiplication: Knowing factors helps us multiply and divide efficiently and understand important arithmetic properties.

General facts

A common factor is a factor that two or more numbers have in common. Finding common factors can help you simplify fractions and solve other mathematical problems. To find the common factors of two numbers:

Example

Let's find the common factors of 8 and 12.

Factors of 8: 1, 2, 4, 8

Factors of 12: 1, 2, 3, 4, 6, 12

Comparing these lists we see that the common factors are 1, 2, and 4.

Greatest common factor (GCF)

The greatest common factor is the largest number that is a factor of two or more numbers. It is extremely useful in simplifying fractions or finding prime factors.

Example

Let's find the GCF of 18 and 24.

Factors of 18: 1, 2, 3, 6, 9, 18

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

The common factors are 1, 2, 3, and 6. The largest of these is 6, so the GCF of 18 and 24 is 6.

Prime factorization

Prime factorization is breaking down a number into its most basic building blocks: its prime numbers. Prime numbers are numbers greater than 1 that are only divisible by themselves and 1.

Example

Let's prime factorize 18.

1. Divide 18 by the smallest prime factor (2): 18 ÷ 2 = 9
2. 9 is not divisible by 2, so use the next smallest prime number 3: 9 ÷ 3 = 3
3. 3 is a prime number, so we stop here.

Thus, the prime factorization of 18 is 2 × 3 × 3 You can also write this as 2 × 32.

Visual representation of prime factorization

18 2 9 3 3

Conclusion

Understanding factorization is very important in math. It enables you to decompose numbers into simpler forms, identify similarities between different numbers, and solve complex problems more easily. These skills will help you with more advanced topics as you progress in learning math.

In short, factors are like the pieces of a puzzle that fit together to form the world of numbers. Becoming proficient at finding factors not only strengthens your mathematical foundation but also enhances your problem-solving abilities for future mathematical endeavors.


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Understanding Factors

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