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 and Composite Numbers


Understanding prime and composite numbers is an important concept in learning math. In this explanation, we'll learn what these terms mean, how you can recognize each type of number, and provide many examples and visuals to make your learning experience interesting and comprehensive.

Introduction to prime numbers

Prime numbers are numbers greater than 1 that have no divisors other than 1 and itself. This means that a prime number cannot be evenly divided by any other number other than 1 and the number itself. Let us look at some examples to understand prime numbers more clearly.

Examples of prime numbers

  • The only two divisors of the number 2 are 1 and 2. Therefore, 2 is a prime number. It is also the smallest prime number and the only even prime number.
  • Number 3: The divisors of 3 are 1 and 3. No other number divides 3 evenly, so it is a prime number.
  • Number 5: The divisors of 5 are 1 and 5, which makes it a prime number.
  • Number 7: Its divisors are 1 and 7, so 7 is a prime number.
  • Number 11: The divisors of 11 are 1 and 11, which confirms it to be a prime number.
2 3 5 7 11

What makes prime numbers special?

Prime numbers are the building blocks of all numbers. Any number can be expressed as a product of prime numbers. This is known as prime factorization. For example, the number 18 is not a prime number, but it can be expressed as a product of prime numbers like this:

18 = 2 × 3 × 3

Understanding prime numbers helps in various aspects of mathematics, including cryptography, where they play a vital role in keeping information secure.

Introduction to mixed numbers

Composite numbers are numbers greater than 1 that are not prime. This means that composite numbers have more than two divisors. Let's look at some examples of composite numbers.

Examples of mixed numbers

  • The divisors of number 4: 4 are 1, 2, and 4. Since it has more than two divisors, it is a composite number.
  • Number 6: The divisors of 6 are 1, 2, 3, and 6, so it is a composite number.
  • Number 8: Its divisors are 1, 2, 4 and 8, making it composite.
  • Number 9: Its divisors are 1, 3 and 9; so it is composite.
  • Number 10: The divisors are 1, 2, 5 and 10. So it is a composite number.
4 6 8 9 10

Identifying prime and composite numbers

To determine whether a number is prime or composite, follow these simple steps:

  1. If the number is less than 2, it is neither prime nor composite. For example, 0 and 1 are neither.
  2. Check divisibility by smaller numbers. If the number is divisible only by 1 and itself, then it is prime.
  3. If a number can be divided evenly by any other number (other than 1 and itself), then the number is composite.

Example: Is 17 a prime number?

Let's determine whether 17 is a prime number:

  • First, check divisibility by numbers smaller than 17.
  • The number 17 cannot be divided evenly by any number other than 1 and 17.
  • Thus, 17 is a prime number.

Example: Is 16 a composite number?

Now let's check if 16 is a composite number:

  • Check divisibility by numbers smaller than 16.
  • 16 is evenly divided by 1, 2, 4, 8 and 16.
  • Since 16 has more than two divisors, it is composite.

Prime and composite numbers in nature and beyond

Prime numbers are not just a mathematical curiosity; they are found in nature and have practical applications. For example, the arrangement of leaves around the stem and the branching patterns of trees are often based on the Fibonacci sequence, which includes prime numbers.

In technology, prime numbers are important for data encryption methods that keep our data secure when shopping online or sending private information. This is because prime numbers are used to create keys that are difficult to break. The higher the prime number, the more secure the encryption.

Mixed examples: prime or composite?

Let's test your understanding with the following examples. Determine whether each number is prime or composite.

Example 1: Number 29

Check divisibility by numbers smaller than 29. Since 29 has no divisors other than 1 and 29, it is a prime number.

Example 2: Number 20

Check divisibility by numbers smaller than 20. It is divisible by 1, 2, 4, 5, 10 and 20, so it is divisible.

Another way to identify: Sieve of Eratosthenes

An ancient technique known as the Sieve of Eratosthenes helps identify primes up to any given number. Follow these steps:

  1. Make a list from 2 to the largest number that interests you.
  2. Select the smallest number in the list and mark it as a prime number.
  3. Cross out all multiples of this smallest number from the list.
  4. Move to the next number on the list and repeat the process.
  5. Continue until you've processed all the numbers.

Example using numbers from 2 to 30:

Basic numbers: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30
Step 1 (Mark 2 as prime number, cross out its multiples): 2 (prime number), 3, _, 5, _, 7, _, 9, _, 11, _...
Step 2 (Mark 3 as a prime number, cross out its multiples): 2 (prime), 3 (prime), _, 5, _, 7, _, _, _,...
Continue until the whole process is completed.
Last prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Conclusion

Prime and composite numbers are a fundamental concept in mathematics, helpful not only for mathematical calculations and theory but also for its applications in real-world scenarios such as cryptography and nature. We hope this comprehensive guide has shed some light on how these numbers are identified and what their significance is in the broader landscape of numbers.

Have fun learning, and use your knowledge of prime and composite numbers to better explore and understand the fascinating world of mathematics!


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Prime and Composite Numbers

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