Composite Numbers

An integer can be generated by multiplying the two smallest positive integers and it contains at least one divisor other than one and itself is called a composite number. Each positive integers is either prime, composite or the unit 1. Composite numbers are the numbers that are neither prime nor unit .

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 has only two factors, 1 and itself.
  • If the number has greater than two factors, then it is a composite number.

Consider the example, 10 is a composite number. Because it is the product of the two smallest integers 2 x 5.

Difference between Prime and composite numbers

Prime Numbers

Composite Numbers

The numbers that can be divided by 1(one) and itself are called prime numbers.It has only two factors.one is the number 1 and the other is the number itself

All the numbers others than prime numbers except 1, and it has more than two factors are called composite 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 numbers.

But it is different for number 4. The divisors of 4 are 1,2,4. So this number satisfies the condition of a composite number as mentioned above. Besides 1 and 4, 2 is also a divisor. 4 is also the smallest composite number. The number 6 is the next composite number after 4 . It has as the factors like 1,2,3,6.

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

Kushagra is drawing a railway track on paper as a part of his project. He asked Sarosh to draw a line parallel to the given line. Sarosh said that we can only construct a line parallel to the given line using alternate angles concept. Is this true?