How to find out if a number is a prime number?

How to find out if a number is a prime number?
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In this lesson, we will learn about prime  and composite numbers, how to find if a number is prime or not, prime number definition, prime number examples, and interactive questions at the end. 

Watch this video to know what prime numbers are,

Lesson Plan

How to Know if a Number Is Prime or Not?

A number that cannot be divided into equal groups is called a prime number. In other words, a number that is divisible only by 1 and itself is called a prime number.

So what do we call a number that is not prime? 

A number that has factors other than one and itself is called a composite number.

Definition

Any whole number that is divisible only by 1 and itself is called a prime number.

For example, 5 has only two factors: 1 and 5.

Prime number groups

We cannot divide 5 into equal groups.

5 can be factorized as:

\(\begin{align} 5 = 1\times5\end{align}\)

A composite number has many other factors other than 1 and itself.

For example, the number 6 has 1,2,3, and 6 as factors. 

Composite number groups

6 can be factorized as

\(\begin{align} 6 = 1\times6\end{align}\)

\(\begin{align} 6 = 3\times2\end{align}\)

Since 6 has more than two factors (other than 1 and 6), it is a composite number.

Examples of Prime Numbers

Some examples of prime numbers are 2,3,5,7,11,17.

Is 1 a Prime Number or a Composite Number?

1 is neither a prime nor a composite number.

Since 1 has only 1 factor, it cannot be a prime number.

It is not composite because it does not have more than two factors.


How to Determine if a Number is Prime or Not?

A prime number has exactly two factors. They are 1 and the number itself.

For example,

7 and 17 factor tree

7 and 17 have exactly two factors. Therefore, they are prime numbers.

Whereas, the number 6 has four factors (1,2,3,6)

Factors of 6

Therefore, 6 is a composite number.

Twin Prime Numbers

Any two prime numbers that have one composite number in between them are called twin prime numbers. 

For example,

(3,5), (5,7), (11,13) are twin prime numbers.

Co-Prime Numbers

A pair of numbers that have no common factors other than 1 are called co-prime numbers. They can have both prime and composite numbers.

For example,

(5,9), (7,11), (18,33), (23,49)

 
important notes to remember
Important Notes
  1. A prime number has exactly two factors.
  2. 1 is neither a prime nor a composite number.
  3. A composite number has more than two factors.

Prime Numbers from 1 to 100

There are 25 prime numbers between 1 and 100. 

They 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, and 97.

Observe the following table which shows the prime numbers from 1 to 100 listed in groups.

Prime numbers between 1 and 10 2, 3, 5, 7
Prime numbers between 11 and 20 11, 13, 17, 19
Prime numbers between 21 and 30 23, 29
Prime numbers between 31 and 40 31,37
Prime numbers between 41 and 50 41,43,47
 Prime numbers between 51 and 100 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Prime Numbers Chart

Here is the list of prime numbers from 1 to 100.

Prime numbers chart


Prime Number Calculator From 1 To 100

Try out the prime number calculator to find the prime numbers from 1 to 100 by using the Sieve of Eratosthenes Algorithm.

1 is struck off as it is neither prime nor composite.

The multiples of numbers 2,3,5,7,11 are struck off. 

The remaining numbers are prime. 


Smallest Prime Number

The smallest prime number is 2

It is the only even prime number. 


Largest Prime Number

The largest prime number cannot be determined, but the largest prime number known till date is \(\begin{align}2^82,589,933 \:-1 \end{align}\) having \(\begin{align}\:24,862,048 \end{align}\)  digits.

 
tips and tricks
Tips and Tricks
  1. 0 and 1 are not prime numbers.
  2. Out of all the prime numbers, 2 is the only even prime number.
  3. To check if a number is prime or not, start dividing the number by 2, if it is divisible then it is not a prime number. Repeat the division by the consecutive prime numbers like 3,5,7,11 and so on. If they are divisible by any of these numbers then we know that they are not prime.

Solved Examples

Example 1

 

 

Is 8 a prime number?

Solution

The factors of 8 are 1,2,4,8

We can see that 8 has more than two factors (other than 1 and 8);

Hence, 8 is not a prime number.

8 is not a prime number.
Example 2

 

 

Find the list of prime numbers between 111 to 120

Solution

Let us list the factors of all the numbers from 111 to 120

Factors of \(\begin{align}111 - 1,3,37,111\end{align}\)

Factors of \(\begin{align}112 - 1, 2, 4, 7, 8, 14, 16, 28, 56, 112\end{align}\)

Factors of \(\begin{align}113 - 1,113\end{align}\) (113 has only 2 factors - 1 and 113)

Factors of \(\begin{align}114 - 1, 2, 3, 6, 19, 38, 57, 114\end{align}\) 

Factors of \(\begin{align}115 - 1, 5, 23, 115\end{align}\) 

Factors of \(\begin{align}116 - 1, 2, 4, 29, 58, 116\end{align}\) 

Factors of \(\begin{align}117 - 1, 3, 9, 13, 39, 117\end{align}\) 

Factors of \(\begin{align}118 - 1, 2, 59, 118\end{align}\) 

Factors of \(\begin{align}119 -  1, 7, 17, 119\end{align}\) 

Factors of \(\begin{align}120 - 1, 2, 3, 4, 5, 6, 8, 10,\end{align}\)

\(\begin{align} 12, 15, 20, 24, 30, 40, 60, 120 \end{align}\)

So, we can conclude that \(\begin{align}113\end{align}\) is a prime number.

\(\begin{align}\therefore\:113\end{align}\) is the only prime number between 111 and 120.
Example 3

 

 

Which is the largest two-digit prime number?

Solution

The largest two-digit number is 99

99 has 1, 3, 9, 11, 33, 99 as factors.

The next lower number is 98

98 has 1, 2, 7, 14, 49, 98  as factors.

We further go one number down to 97

97 has 1 and 97 as factors.

Since 97 has only two factors, we can clearly say that it is the largest two-digit prime number.

97 is the largest two-digit prime number.

Interactive Questions

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

 
 
 
 
 

 


Let's Summarize

This lesson targeted the concept of knowing whether a number is prime or not. Knowledge of factors and multiples are essential to learn about prime numbers. Trying out the solved examples would enrich your knowledge on the subject. Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever. Here lies the magic with Cuemath.

About Cuemath

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.


FAQs on Identifying Prime Numbers

1. How can you tell if a number is prime or composite?

If a number has only two factors (1 and itself), then it is a prime number. If a number has more than two factors it is a composite number.

2. Can we predict prime numbers?

We cannot predict whether a number is prime or not. We need to factorize it to get the answer.

3. Why is 1 not a prime number?

1 is neither a prime nor a composite number because a prime number should be greater than 1 and should have two factors.

4. What is the smallest odd prime number?

3 is the smallest odd prime number.

  
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