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Composite Numbers
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.
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.
multiplying positive integers will give a composite number
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.