Numbers can be classified on the basis of the number of factors they have. If a number has just two factors - 1 and the number itself, then it is a prime number. However, most numbers have more than two factors, and they are called composite numbers. On this page, we will learn the difference between prime and composite numbers, the smallest composite number, and odd composite numbers. The last one is interesting because there are several odd composite numbers, unlike 2, which is the only even prime number.
|1.||What are Composite Numbers?|
|2.||Properties of Composite Numbers|
|3.||How to Find Composite Numbers?|
|4.||Types of Composite Numbers|
|5.||Smallest Composite Number|
|6.||FAQs on Composite Numbers|
What are Composite Numbers?
Composite numbers can be defined as natural numbers that have more than two factors. In other words, a number which is divisible by a number other than 1 and the number itself, is called a composite number. Let’s learn more about composite numbers with examples.
Examples of Composite Numbers
4, 6, 8, 9, and 10 are the first few composite numbers. Let's take 4 and 6. In the above example, 4 and 6 are called composite numbers because they are made by combining other numbers. This idea is important and we used it in a theorem called the Fundamental Theorem of Arithmetic. Let's proceed to understand the important features of composite numbers.
Properties of Composite Numbers
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Note the properties of a composite number listed below:
- All composite numbers are evenly divisible by smaller numbers that can be prime or composite.
- Every composite number is made up of two or more prime numbers.
Let us have a look at the properties of the composite number 72 in order to understand the concept in a better way.
This figure shows that by multiplying these positive integers we get a composite number.
How to Find Composite Numbers?
In order to find a composite number, we find the factors of the given number. If the number has more than two factors, then it is composite. The best way to figure out a composite number is to perform the divisibility test. The divisibility test helps us to determine whether a number is a prime or a composite number. Divisibility means that a number is divided evenly (with no remainder) by another number.
To do this, check to see if the number can be divided by these common factors: 2, 3, 5, 7, 11, and 13. If the given number is even, then start checking with the number 2. If the number ends with a 0 or 5, then check it by 5. If the number can’t be divided by any of these given numbers, then the number is a prime number. For example, 68 is divisible by 2, which means it has factors other than 1 and 68, so, we can say 68 is a composite number.
Types of Composite Numbers
The two main types of composite numbers in maths are Odd Composite Numbers and Even Composite Numbers. Let us have a look at the two of them individually:
Odd Composite Numbers
All the odd integers which are not prime are odd composite numbers. For example, 9, 15, 21, 25, 27 are odd composite numbers. Consider the numbers 1, 2, 3, 4, 9, 10, 11, 12 and 15. Here 9 and 15 are the odd composites because these two numbers have odd divisors and satisfy the composite condition.
Even Composite Numbers
All the even numbers which are not prime are even composite numbers. For example, 4, 6, 8, 10, 12, 14, 16, are even composite numbers. Consider the numbers 1, 2, 3, 4, 9, 10, 11, 12 and 15 again. Here 4, 10, and 12 are the even composites because they have even divisors and satisfy the composite condition.
Smallest Composite Number
A composite number is defined as a number that has divisors other than 1 and the number itself. Start counting: 1, 2, 3, 4, 5, 6, .... so on. 1 is not a composite number because its sole divisor is 1. 2 is not a composite number because it has only two divisors, i.e., 1 and the number 2 itself. 3 is not a composite number because it has only two divisors, i.e., 1 and the number 3 itself. Let’s look at number 4. Its divisors are 1, 2, and 4. Number 4 satisfies the criteria of a composite number. So, 4 is the smallest composite number.
Example 1: Determine whether 486 is a composite number or not?
The given number is 486. Its factors or divisors are - 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, and 486. This shows that it has factors other than 1 and itself.
∴ 486 is a composite number.
Example 2: Solve the following riddle: "I lie between 30 and 40; I have only two prime factors. The sum of my prime factors is 5; Who am I?"
The sum of the prime factors of this unknown number is 5. We know that the prime numbers whose sum is 5 are 2 and 3. Now, we need to find a number that has 2 and 3 as its only prime factors and which lies between 30 and 40. Let us see the prime factorization of 36: 36 = 2 × 2 × 3 × 3. So, 36 satisfies the given conditions.
∴ 36 is the required number.
FAQs on Composite Numbers
How to Find Composite numbers?
To find whether a given number is composite, we just find the number of factors it has. If it has more than 2 factors, then the number is composite. For example, 4 has three factors, 1, 2, and 4. So, it is a composite number.
Is 2 a Composite Number?
No, 2 is not a composite number, it is the only even prime number. A composite number has more than two factors, other than 1 and the number itself. Here, 2 has only two factors, 1 and 2 itself. Therefore, 2 is a prime number.
What are the Composite Numbers Between 1 and 100?
The composite numbers between 1 and 100 are-
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.
What is a Composite Number and Prime Number?
A number that is divisible by a number other than 1 and the number itself, is called a composite number. For example, 4, 6 are composite numbers. Whereas, a number that is divisible only by 1 and itself is called a prime number, like, 2, 3, and 5.
What is an Odd Composite Number?
All the odd integers (excluding 1) which are not prime are odd composite numbers. For example, 9 and 15 are the odd composite numbers.
What is the Smallest Composite Number?
A composite number has more than two factors, other than 1 and the number itself. Here, 4 satisfies this condition, and there is no other number smaller than 4 which is composite. Therefore, 4 is the smallest composite number.
What is the Difference Between a Prime and a Composite Number?
A prime number has only two factors, 1 and the number itself, whereas, a composite number has more than two factors. For example, 5 has only two factors, 1 and 5, so it is a prime number. Whereas 6 has four factors, 1, 2, 3, and 6, so it is a composite number.