Composite Numbers

Composite numbers are integers which can be generated by multiplying the two smallest positive integers and contains at least one divisor other than number ‘1’ and itself. It is neither a prime number nor a unit. The smallest composite number is 4, which has factors 1, 2 and 4. Therefore, we can also say, any number which is not a prime is a composite one and has more than two factors. This is the general difference between prime and composite numbers. Let us learn now how to figure them out.

Procedures to find whether a given number is prime or composite:

  • Find all the factors of the positive integer
  • A number is said to be prime if it has only two factors, 1 and itself.
  • If the number has more than two factors, then it is a composite.

Consider the example, 10 is a composite number. Because it is the product of the two smallest positive integers 2 x 5 and has factors 1, 2 and 5. Let us discuss more briefly here.

Difference between Prime and composite numbers

Prime Numbers Composite Numbers
It can only be divided by 1 and itself, thus have only two factors. It has more than two factors(1 and itself).
It can only be written as product of two numbers It can be written as the product of two or more numbers
Example: 5 (factors are 1 and 5) Example: 4( factors are 1, 2 and 4)

How to find the Smallest Composite Number?

1 is not a composite number because the sole divisor of 1 is 1. The positive integers 2 and 3 are prime numbers because it can be divided by one and itself. Hence 2 and 3 are not composite.

But in the case of number 4, we have more than two factors. The divisors of 4 are 1,2,4. So this number satisfies the condition of a composite number as mentioned above. After 4, 6 is the next composite positive integer, which has factors 1, 2, 3 and 6.

Hence, 4 is the smallest composite number (Proved).

Odd Composite Numbers

A number that is not divisible by 2 is called an odd number. Similarly, if the positive integer that contains more than two factors but none of which are two, called odd composite numbers.

For example:

Consider the numbers 1, 2, 3, 4, 9, 10, 11,12, and 15 . Here 9 and 15 are the odd composite numbers because those two numbers have the odd divisors and obey the composite number condition.

Composite numbers from 1 to 100

The composite numbers from 1 to 100 include: 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

To learn more about the different types of numbers, download BYJU’S -The Learning App from the Google play store and watch interactive videos.


Practise This Question

If A and B are two sets containing four and two elements, respectively. Then, the number of subsets of the set A×B each having atleast three elements are