Composite number is a number that could be formed by multiplying two or more whole numbers greater than a unit. Example: 4, 6, 9..

Composite numbers are those numbers which have more than two factors and can be divided by more than just 1 and themselves. Composite numbers are so called because they are composed of more than two factors and can be even or odd.

Let us find factors of 12 and 15. The number 12 has factors 4 and 3. 4 could be further factorized into 2 x 2 so, basically 12 has factors 2 x 2 x 3, while 15 has 5 and 3 as factors and so they are considered as composite numbers.

A composite number is a positive term which has more than two different factors. Unlike a prime number which has only two factors one and the number itself, a composite number has various other numbers as its factors.

Example: 4, 6, 8, 10, 12, 14...... are composite numbers because these numbers are composed of the other numbers. 0 and 1 are neither prime nor composite numbers.

A composite number is a positive whole number which can have three or more divisors or factors. Other numbers are called prime numbers. Hence composite numbers can be said to be opposites of prime numbers. So, it can be said that all composite numbers are non-primes. Now, the numbers 0 and 1 are not taken as composite numbers.

So, a composite number can be redefined as "a non-prime number with has only one or more prime factors". Also, 2 is the only even prime number. So composite numbers can be redefined as "numbers with both even and odd numbers which are greater than 2." Again the smallest composite number is 4.

For example:

The number 9 has factors 1, 3 and 9; hence it is a composite number.

14 has factors 1, 2, 7, 14 (4 factors), so it is a composite number.

The first composite numbers can be written as:
4, 6, 8, 9, 10, 12...

A method to determine composite numbers is Sieve of Eratosthenes. This is mostly used to find prime numbers. The numbers that are taken will be composite numbers. The method is a follows:

  1. Write the list of numbers starting from 2 and going up to any limit, say up to 100.
  2. The first prime number is 2. Keep it as such and cross out all the multiples of 2.
  3. The next unmarked number is 3. Keep it as such and cross out it's multiples.
  4. Next, its five. Cross out its multiples.
  5. Similarly, we do it up to 100.
  6. Taking all the crossed out numbers, we get a list of composite numbers.

The numbers listed in blue in the chart below are composite numbers.

Composite Numbers 1-100

Composite Number 1-100

Examples on Composite Numbers


Here are some examples for composite numbers

Example :

In the following which of the following is prime.
63, 21, 7, 19

Solution:

i) The factors of 63 are 1, 3, 7, 9, 21 and 63.
So, it is not a prime number.

ii) The factors of 21 are 1, 3, 7 and 21
So, it is not a prime number.

iii) The factors of 7 are 1 and 7
So, it is a prime number.

iv) The factors of 19 is 1 and 19.
So, it is a prime number.