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