How to find the Factors of a Number

Once you clearly understand what a factor really is, you are ready to learn how to find the factor of a number in mathematics. So, let’s know how to find the factors of a number by a step by step procedure.

There is a simple procedure to find the factors of any number in mathematics.

1. Use the long division method to divide a number by each natural number, starts from one.
2. Continue the process of division until we see a reminder.
3. If there is a remainder, then the divisor number cannot be a factor of dividend number. Otherwise, it is a factor of that number.
4. Repeat the above three steps until we divide a number by the same number.

The above four steps may confuse you theoretically, but you can easily understand here by the following simple and understandable examples.

Example

Let’s learn how to find the factors of a number $3$.

The first natural number is $1$ in mathematics and let’s divide the number $3$ by $1$ firstly.

The remainder is zero, which means there is no remainder when the number $3$ is divided by $1$. It means, the number $1$ divides $3$ completely. Therefore, the number $1$ is called a factor of $3$.

The second natural number is $2$ and let’s repeat the same procedure to divide the number $3$ by $2$.

The remainder is one, which means there is a remainder when the number $3$ is divided by $2$. It means, the number $2$ does not divide $3$ completely. Therefore, the number $2$ is not a factor of $3$.

The third natural number is $3$ and let’s repeat the same process once again to divide the number $3$ by itself.

The remainder is zero, which means there is no remainder when the number $3$ is divided by the same number. It means, the number $3$ divides $3$ completely. Therefore, the number $3$ is called a factor of $3$.

The process of division should be stopped here because the natural numbers greater than $3$ are $4, 5, 6, \cdots$ and they cannot divide the number $3$ completely.

Conclusion

1. There is no remainder when the numbers $1$ and $3$ divide the number $3$. It means, the numbers $1$ and $3$ divide the number $3$ completely. So, the numbers $1$ and $3$ are called the factors of $3$.
2. There is a remainder when the number $2$ divides the number $3$. It means, the number $2$ does not divide the number $3$ completely. So, the number $2$ is not a factor of $3$.

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