How to Find Composite Numbers?

In Mathematics, composite numbers are numbers that have more than two factors. Composite numbers are exactly the opposite of prime numbers, which have only two factors, i.e. \(1\) and the number itself.

Step by step guide to composite numbers

Composite numbers can be defined as natural numbers that have more than two factors. In other words, a number that is divisible by a number other than \(1\) and the number itself is called a composite number.

Properties of composite numbers

A composite number is a positive integer that is obtained by multiplying two smaller positive integers. Characteristics of a composite number are 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’s take a look at the properties of composite number \(72\) to better understand the concept.

How to find composite numbers?

To find a composite number, we find the factors of the given number. The best way to determine a composite number is to do a divisibility test. The divisibility test helps us determine if the number is prime or composite. Divisibility means that one number is divided completely (without 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 in \(0\) or \(5\), check it with \(5\). If the number cannot be divided by any of these given numbers, then the number is a prime number. For example, \(42\) is divisible by \(2\), which means it has factors other than \(1\) and \(42\), so, we can say \(42\) is a composite number.

Types of composite numbers

The two main types of composite numbers in mathematics are odd composite numbers and even composite numbers.

Odd composite numbers

All the odd numbers which are not prime are odd composite numbers. For example, \(9, 15, 21, 25\), and \(27\) are odd composite numbers.

Even composite numbers

All the even numbers that are not prime are even composite. For example, \(4, 6, 8, 10, 12, 14,\) and \(16\), are even composite numbers.

Smallest composite number

A composite number is a number that has a divisor other than \(1\) and the number itself. . Now, as we start counting: \(1, 2, 3, 4, 5, 6,\) …. so on, we see that \(1\) is not a composite number because the only divisor against it 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, \(1\) and the number \(3\) itself. However, when we get to the number \(4\), we know that the divisors are \(1, 2\), and \(4\). Number \(4\) meets the criteria for a composite number. Therefore, \(4\) is the smallest compound number.

Composite Numbers – Example 1:

Is \(486\) a composite number or not?

Solution:

Its factors 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. Therefore, \(486\) is a composite number.

Exercises for Composite Numbers

which of the number is a composite number?

1. \(\color{blue}{73}\)
2. \(\color{blue}{51}\)
3. \(\color{blue}{42,059}\)
4. \(\color{blue}{991}\)

1. \(\color{blue}{Not}\)
2. \(\color{blue}{Yes}\)
3. \(\color{blue}{Yes}\)
4. \(\color{blue}{Not}\)