What are composite numbers: Definition, and examples.

Mathematics is a subject that involves interesting concepts of numbers. The subject is one of the core requirements in the Montessori preschool curriculum to develop an early curiosity among the students.

Among the various fascinating concepts of mathematics, composite numbers hold a significant place due to their unique properties. Understanding the main concept of composite numbers is essential to learn the higher mathematical concepts. A strong understanding of all composite numbers makes many mathematical concepts easier to grasp.

Let us explore the definition, examples, and properties of composite numbers for a better understanding of the concept.

What are Composite Numbers?

In mathematics, composite numbers are those which have more than two factors. In other words, if a number is divisible by a number other than 1 and itself, it becomes a composite number.

For example, number 4 is a composite number as it can be divided by 1,2 and 4. It has more than two factors. On the other hand, number 2 is only divided by 1 and itself, which makes it a prime number.

To understand the concept in a simpler tone, composite numbers are opposite from the prime numbers. A prime number has only two factors, the number 1 and the number itself. Composite numbers, thus, have more than two factors.

Properties of Composite Numbers

Composite numbers have the following properties that make them apart from prime numbers:

• Multiple factors:

Unlike prime numbers, composite numbers have more than two factors. It is divisible by 1, itself, and any other number.

• Evenly divisible:

Composite numbers can be evenly divisible by their factors.

• Factor of Self:

Interestingly, each composite number is a factor of itself.

• Divisible by other composite numbers:

Composite numbers are also divisible by other composite numbers.

• Two prime number factors:

Every composite number includes at least two prime numbers as its factors. For example: 10 = 2 X 5, where 2 and 5 both are prime numbers.

Examples of Composite Numbers

Let us look at the various examples of composite numbers 1 to 100 to get a clear understanding of their properties. These are some of the examples of composite numbers:

• Number 4: Divisible by 1, 2 and 4
• Number 6: Divisible by 1, 2, 3 and 6
• Number 8: Divisible by 1, 2, 4 and 8
• Number 9: Divisible by 1, 3 and 9
• Number 10: Divisible by 1, 2, 5 and 10
• Number 12: Divisible by 1, 2, 3, 4, 6 and 12
• Number 15: Divisible by 1, 3, 5 and 15
• Number 18: Divisible by 1, 2, 3, 6, 9 and 18, and so on.

Each composite number mentioned is greater than 1 and also has multiple factors.

Types of Composite Numbers

Composite numbers are of two main types:

• Odd Composite Numbers:

The odd numbers which are not prime numbers are known as the odd composite numbers. These numbers are not divisible by 2, but other numbers like 3 or 5. For example: 9, 15, 21, 25, 27, etc. are some of the odd composite numbers.

• Even Composite Numbers:

The even numbers which are not prime numbers and are divisible by 2 are the even composite numbers. For example, the numbers 4, 6, 8, 10, and 12 are all even composite numbers as they are all divisible by 2 and have more than two factors.

How to Identify Composite Numbers?

To identify composite numbers, it is important to consider the factors of the number. If the number has more than two factors, then it is a composite number.

One of the best ways to identify if the number is prime or composite is to perform a divisibility test. Divisibility test means that the number should be completely divided by other numbers than 1 and itself with no reminders.

For example: Let us check if the number 14 is a composite number or not using a divisibility test. The factors of number 14 are – 1, 2, 7 and 14. Since the number has more than two factors, it is a composite number.

Let us take another number, say, 68. The common factors of 68 are – 1, 2, 4, 17, 34 and 68 which are more than two. Thus, we can say that the number 68 is a composite number.

Prime Factorisation of Composite Numbers

To understand this in simple words, prime factorisation is the process to break down the composite number into its prime factors. Besides the other critical mathematical concepts, prime factorisation is an essential part of the curriculum in the best preschool in Ahmedabad.

Every composite number can easily be expressed as the product of prime numbers. Let us understand this with an example. For example:

• For number 12: The prime factorisation is 2 X 2 X 3
• For number 18: The prime factorisation is 2 X 3 X 3
• For number 30: The prime factorisation is 2 X 3 X 5

Prime factorisation is important to simplify fractions and finding the greatest common divisors in complex mathematical problems.

Importance of Composite Numbers in Mathematics

Composite numbers are essential in mathematics as the concept is used in more complex problems. The numbers have significant importance in the understanding and practical applications of various other mathematical concepts. They play an essential role in calculating interest rates, number theory, prime factorisation, and in simplifying fractions.

Composite numbers are also used to understand the structure of the integers. Additionally, they are also used in discovering patterns related to perfect numbers and divisors. Understanding the concept of composite numbers is important for students to excel in the field of mathematics.

Common Misconceptions About Composite Numbers

Despite the popularity of composite numbers, there are many misconceptions about them. Some of the common misconceptions about the composite numbers 1 to 100 and more are as following:

• All even numbers are composite:

This is not true. All even numbers greater than 2 are composite; 2 itself is a prime number having 2 factors, 1 and 2.

• A composite number is always divisible by 3:

This is also incorrect. For example, the number 25 is a composite number but is not divisible by 3.

• Prime and composite numbers are the same:

Many people confuse prime numbers with composite numbers. However, prime numbers have only two factors while the composite numbers have more than two factors.

Practice Problems and Solutions

• Is 15 a composite number?

Yes, 15 is a composite number as it has more factors than two which are 1, 3, 5 and 15.

• Find the prime factorisation for the number 60?

The prime factorisation for the number 60 is 2 X 2 X 3 X 5

• What are the divisors of 28?

The divisors of 28 include 1, 2, 4, 7, 14 and 28. Since it has more than 2 factors, this makes 28 a composite number.

• Check if 23 is a composite number.

To check if 23 is a composite number, let us find its factors. The number 23 has only 2 factors, 1 and 23; thus, it is not a composite number. This is a prime number.

• What is the product of the first 5 composite numbers?

4, 6, 8, 9, and 10 make the very first 5 composite numbers. Hence, the product would be: 17280.

Conclusion

Composite numbers are one of the fundamental concepts in mathematics. It is important to get a deeper and clear understanding of the concept to solve the other complex mathematical problems. Understanding composite numbers can unlock a world of mathematical possibilities.

As one of the top schools in Ahmedabad, GIIS is committed to providing an engaging learning experience to students. We help our students master the concept of composite numbers and other mathematical concepts using interactive lessons and activities. Join GIIS Ahmedabad and give your child the innovative methods to become successful in mathematics and beyond.