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 ↓


Prime Factorization


Mathematics is an exciting world full of numbers and their amazing properties. Today, we are going to explore a wonderful concept called “Prime Factorization”. It is like solving a mystery where we break down numbers to find their hidden properties. Let's discover the building blocks. Are you ready to become a number detective? Let's get started!

What is factorization?

Before we talk about prime factorization, let us understand what is meant by factorization. In simple terms, factorization is breaking down a number into smaller numbers that can be multiplied together to get the original number. These smaller numbers are called prime factorization. The numbers are called "multiples."

Example:

Consider the number 12 It can be factored as follows: 
12 = 1 × 12
12 = 2 × 6
12 = 3 × 4
These pairs (1 and 12, 2 and 6, 3 and 4) are all factor pairs of 12 because when you multiply them the result is 12.

Understanding prime numbers

To understand prime factorization, we need to know what prime numbers are. A prime number is a number greater than 1 that can be divided evenly only by 1 and itself.

Examples of prime numbers:

  • 2 - the only even prime number that is divisible by 1 and 2.
  • 3 – Divisible by 1 and 3.
  • 5 – Divisible by 1 and 5.
  • 7 – Divisible by 1 and 7.
  • 11 – Divisible by 1 and 11.
  • 13 – Divisible by 1 and 13.

Introduction to prime factorization

Now that we understand what prime numbers are, let's get to the main topic: prime factorization. Prime factorization is breaking down a number into its most basic building blocks, which are prime numbers. These prime numbers are multiplied together to get a number. By doing this you will get the original number back.

Visual example:

Let's consider the number 18 We want to break it down into its prime factors: 
Start by finding the two factors of 18:
18 = 2 × 9

Now split 9 into its factors:
9 = 3 × 3

So, the prime factorization of 18 is:
18 = 2 × 3 × 3
This means that the prime factors of 18 are 2 and 3.

Steps in prime factorization

Let us understand the steps to find the prime factorization of any number:

  1. Start with the smallest prime number: Start with the smallest prime number, which is 2 Check if the number is divisible by 2 If it is, divide it and continue with the result until it is divisible by 2 should not be divisible by.
  2. Move on to the next prime: If the number is no longer divisible by 2, move on to the next smallest prime number, such as 3, and check again. Continue this process with 5, 7, 11, and so on, until you cannot divide further.
  3. Complete the factorization: When the number is completely broken down into prime numbers, you have prime factors.

Example:

Let's find the prime factorization of 60 Start with 2: 
60 ÷ 2 = 30
30 ÷ 2 = 15

Now, 15 is not divisible by 2, so we move on to 3:

15 ÷ 3 = 5

Now, 5 is already a prime number.

Putting everything together, the prime factorization of 60 is:

60 = 2 × 2 × 3 × 5

Why is prime factorization important?

Prime factorization is important for several reasons:

  • Finding LCM or GCF: It helps to find Least Common Multiple (LCM) and Greatest Common Factor (GCF) of two or more numbers.
  • Simplifying Fractions: It is used to simplify fractions to their lowest terms.
  • Problem Solving: It helps in solving various mathematical problems where understanding the structure of numbers is important.

Practice exercises

Try to find the prime factors of the following numbers:

  1. Find the prime factors of 24.
  2. What are the prime factors of 36?
  3. Divide 45 into its prime factors.
  4. Find the prime factors of 100.

Exercise answers

1. Prime factors of 24:

Start with 2:
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3

3 is a prime number.

The prime factors of 24 are: 2 × 2 × 2 × 3

2. Prime factors of 36:

Start with 2:
36 ÷ 2 = 18
18 ÷ 2 = 9

Go to 3:
9 ÷ 3 = 3

3 is a prime number.

The prime factors of 36 are: 2 × 2 × 3 × 3

3. Prime factors of 45:

Start with 3:
45 ÷ 3 = 15
15 ÷ 3 = 5

5 is a prime number.

The prime factors of 45 are: 3 × 3 × 5

4. Prime factors of 100:

Start with 2:
100 ÷ 2 = 50
50 ÷ 2 = 25

Go to 5:
25 ÷ 5 = 5

5 is a prime number.

The prime factors of 100 are: 2 × 2 × 5 × 5

Conclusion

Prime factorization may seem like a complicated topic at first glance, but once you understand it, it is like unlocking the secret code behind numbers. By practicing, you will become more efficient in breaking down any number into its prime factors. You will become confident. Keep exploring the wonderful world of numbers, and enjoy your mathematical journey!

Happy factoring!


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Prime Factorization

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