What are Prime Numbers?
Prime numbers are the natural numbers, which are greater than 1 and have exactly two factors that are 1 and the number itself. Then, what about the numbers that have more than two factors? They are called composite numbers.
All prime numbers are odd numbers except the number 2, which is said to be the smallest and the only even prime number. Prime numbers cannot be divided into equal parts.
Properties of Prime Numbers
Now, let’s take a look at the properties of prime numbers.
- Any number greater than 1 is divisible by at least one prime number
- The only two factors of a prime number are 1 and the number itself
- Two prime numbers will always be coprime to one another
- Every even natural number greater than 2 can be expressed as the sum of two prime numbers
Now that we have an understanding of prime numbers, it is better to memorize the prime numbers from 1 to 100.
Prime Numbers Between 1 to 100
There are 25 prime numbers between 1 to 100. The table lists the prime numbers between 1 and 100.
Determining Whether a Number is a Prime Number
In order to determine whether a number is prime or not, we need to find the factors of that number.
A ‘Factor Tree’ is one of the most common ways to find the factors of any number. It is a special diagram that shows how all the factors of a number can be derived until we get a list of prime factors.
The ends of the factor tree will always have the prime factors of the given number. For instance, let us see if the number 30 is a prime number or not, using a factor tree.
Here, 30 has more than 2 factors and the prime factors are 2, 3, and 5. Hence, it is not a prime number.
[Note: Most of the numbers may have more than one factor tree. However, the prime factors in every factor tree are the same.]
Solved Prime Number Examples
Example 1:
Check whether 55 is a prime number or not.
Solution:
Given number is 55.
Now, list all the factors of 55 as, 1, 5, 11 and 55.
Since, 55 has more than the two factors it is not a prime number.
Example 2:
There are 23 students enrolled in a class. Can the teacher divide the students into equal groups? Explain.
Solution:
It is stated that there are 23 students in a class.
We can find out if the teacher can divide the class into equal groups or not by determining whether 23 is prime or not.
So, let us construct a factor tree of 23.
As we can see, 23 does not have any other factor apart from 1 and 23. So, 23 is a prime number. So, 23 cannot be divided into equal parts.
Therefore, the teacher cannot divide the class into equal groups.
Example 3:
Find the prime factors of 108 with the help of a factor tree.
Solution:
Given number is 108.
The factor tree for 108 is:
So the prime factorization of 108 is 2 \(\times\) 2 \(\times\) 3 \(\times\) 3 \(\times\) 3.
Therefore the prime factors of 108 are 2 and 3.
A prime number is a number that is greater than 1 and has exactly two factors, 1 and the number itself. A composite number is a number that is greater than 1 but has more than two factors.
Since 1 has only one factor, that is 1 itself, it is neither a prime number nor a composite number.
There are three types of prime numbers in math.
- Even prime numbers
- Twin prime numbers
- Coprime numbers
Even prime numbers are those that are divisible by 2 and have only two factors. There is only one even prime number, which is 2.
Coprime numbers are a pair of numbers that have only a single common factor between them. For instance, 5 and 7 are coprimes as there is only one common factor between them, which is 1.