A natural number that is divisible only by one and itself is called a prime number.

The prime numbers are natural numbers but all natural numbers are not prime numbers. There are two different theories to determine the prime numbers from the natural numbers.

- Division method
- Factoring method

Now, let’s study both methods to learn how to determine the prime numbers from natural numbers.

There are some natural numbers, which are only divisible by one and themselves. They are called as prime numbers but the remaining natural numbers are also divided by one or more other natural numbers. So, they cannot be called as prime numbers.

$5$ and $6$ are two natural numbers.

$(1) \,\,\,\,\,\,$ $\dfrac{5}{1} \,=\, 5$

$(2) \,\,\,\,\,\,$ $\dfrac{5}{5} \,=\, 1$

The natural number $5$ is a prime number because it is divided by $1$ and $5$ but cannot be divided by any other natural number.

$(1) \,\,\,\,\,\,$ $\dfrac{6}{1} \,=\, 6$

$(2) \,\,\,\,\,\,$ $\dfrac{6}{6} \,=\, 1$

It seems, the natural number $6$ is a prime number but it is not because it can be divided by some other natural numbers $2$ and $3$ as well.

$(3) \,\,\,\,\,\,$ $\dfrac{6}{2} \,=\, 3$

$(4) \,\,\,\,\,\,$ $\dfrac{6}{3} \,=\, 2$

Therefore, $5$ is a prime number but $6$ is not a prime number.

Every natural number can be written as two or more factors. If a natural number has only two factors, then it is called as a prime number.

$7$ and $10$ are two natural numbers.

$7 \,=\, 1 \times 7$

The factors of $7$ are two and they are $1$ and $7$. So, the natural number $7$ is a prime number.

The natural number $10$ can be factored in three ways possibly.

$(1) \,\,\,\,\,\,$ $10 \,=\, 1 \times 10$

$(2) \,\,\,\,\,\,$ $10 \,=\, 2 \times 5$

$(3) \,\,\,\,\,\,$ $10 \,=\, 1 \times 2 \times 5$

The factors of $10$ are $1, 2, 5$ and $10$. So, it has four factors. Therefore, the natural number $10$ is not a prime number.

Latest Math Topics

Jan 06, 2023

Jan 03, 2023

Jan 01, 2023

Dec 26, 2022

Dec 08, 2022

Latest Math Problems

Nov 25, 2022

Nov 02, 2022

Oct 26, 2022

Oct 24, 2022

Sep 30, 2022

A best free mathematics education website for students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Learn how to solve the maths problems in different methods with understandable steps.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved