The difference between prime number and composite number is that prime numbers are natural numbers with just the number itself and one other element.
On the other hand, Natural numbers with more than two elements are known as composite numbers.
Let’s discuss what prime and composite numbers are:
Table of Contents
Before we start, let’s define what “natural numbers” mean. The group of numbers 1 to 10 is known as natural numbers.
Prime numbers and composite numbers are two categories of natural numbers.
Prime numbers are whole numbers that, in a closed system, can only be divided by one and by themselves (resulting in another whole number).
They can be divided by other numbers, but the result will be a rational value (a fraction). Those 2, 3, 5, 7, 11, 13, and 17 are prime numbers.
Prime Numbers from 1 to 100 in mathematics are:
(2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97)
Types of Prime Numbers
There are various prime numbers, and the most important are given below:
1. Balanced Primes
Balanced primes have an equal size gap between the earlier and later prime numbers. For instance, 5, 53, 157, 173, 211, 257, 263, and 373.
2. Gaussian primes
All 1 In – 1 Gaussian primes have the form pn2 > pn-i pn+i, where pn is the nth prime number. The following are some examples: 5, 11, 17, 29, 37, 41, 53, 59, 67, 71, 97, 101, 127, 149, 179
3. Circular Primes
On any cyclic rotation of their digits, circular primes maintain their primacy. 2. 3. 5. 7. 11. 13. 17. 31. 37. 71. 73. 79. 97. 113.
Properties of Prime numbers
- The only even prime number is two. You can divide other even numbers by 2. Therefore, even integers that are divisible by two are not prime numbers.
- The numbers 0 and 1 are not prime.
- It is always possible for two prime numbers to be coprime.
A whole number that has factors besides itself and one is called a composite number. 4, 6, 8, 9, and 10 are composite numbers.
Four has the factors of one, two, and four.
Composite numbers from 1 to 100 in mathematics are:
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.
Properties of Composite Numbers
- There are more than two components in composite numbers.
- By their factors, composite numbers can be divided equally.
- Every composite number has itself as a factor.
- Additionally, composite numbers can be divided by other composite numbers.
Types Of Composite Numbers
- Composite Odd Numbers
- Composite Even Numbers
1. Composite Odd Numbers
An odd composite number is any odd integer that is not a prime number. For instance, the composite numbers 9, 15, 21, 25, 27, and 33 are odd.
2. Composite Even Number
An even composite number is an even integer that is not a prime number. For instance, the composite numbers 4, 6, 8, 10, and 12 are all even.
What is the Difference Between Prime and Composite Numbers?
Mathematicians tried to differentiate between every single number.
They discovered that as a product of primes, every number has a distinct representation (and 1 if needed).
For instance, the number 24 can be written as 2*2*2*3, and the number 32 as 2*2*2*2*2. They are represented in different ways.
As a result, every integer has a different prime number factorization.
The concept of prime and composite numbers is also helpful for learning basic operations like addition, subtraction, and divisibility. Until any mathematical values.
The idea of prime and composite numbers is one of the fundamentals of mathematics.
Prime numbers were utilized in this method, and composite numbers were discovered because we needed names for non-prime numbers.
A prime number is a whole number with only two components, whereas a composite number might have more than two factors. This is the main difference between prime numbers and composite numbers.
Prime numbers have only one divisor (the number itself) and two possible divisors.
While composite numbers are those that have three or more divisors minimum.
This difference causes specific numbers to be prime and others to be composite.
For instance: Because it has two divisors —1 and 47—47, it is prime.
Because it has two divisors —1 and 47—47, it is prime. While 48 has 2, 4, 6, and 8, making it a composite number. A number cannot be both a composite number and a prime number. However, it is either composite or prime.
The only distinction is that they are opposites because composite implies “not prime.”
The number 11 and the prime number itself are the only two divisors.
There are at least 33 divisors for a composite number.
Another key difference between prime and composite numbers is that a prime number cannot be divided into its prime factors, whereas a composite number may.
Although primes cannot be claimed to exist in arbitrarily long sequences of successive numbers, composite numbers can.
While this is not true for composites, the greatest common divisor of any two primes is always 11.
A prime number’s square root is always irrational; it may be an integer for composite numbers.
Huge composite numbers can be created quickly, while large prime numbers are complicated to come by.
Whole numbers that can be divided into other whole numbers in addition to one and themselves are known as composite numbers. 4, 6, 8, 9, 10, 12, 14, 15.
Is 91 a Prime Number?
It is now evident that 91 does not meet the requirements for prime numbers. 91 is a composite number since it meets the requirements for such a number.
The factors of 91 are 1, 7, 13, and 91.
The following are some other categories in which the number 91 falls:
- A natural number
- A positive integer
- An odd number
- A composite number
Is 19 a Prime Number?
Let’s first examine what defines a number as “prime.” A number is a prime number if it only has one other factor, the number itself. The number is composite if there are more than two contributing elements. What do you view19 right now? Is 19 a prime number? “19 is a prime number, yes.” The fact that 19 only has two elements, 1 and 19, makes it a prime number.
Difference Between Prime and Composite Numbers
Highlighting the difference between prime and composite numbers in the following table:
|Prime Numbers||Composite Numbers|
|There are only two components because it can only be divided by one and by itself.||It includes more than two components.|
|The only way to write it is as the product of two numbers.||It can be expressed as the sum of two or more numbers.|
|Example: 3 has factors such as (1, 3).||For example, 6 has the factors 1, 2, 3 and 6.|
The difference between prime and composite numbers is that composite numbers have more than two main factors. They are the prime numbers’ exact reverse. The only two elements in a prime number are 1 and the number itself.