The process of finding the factors of a number is called the factorization of a number.

Once you know the concept of a factor, you should learn how to find the factors of a number mathematically. There is a mathematical procedure to find the factors of a number in mathematics and it is called the factorization (U.S English) or factorisation (U.K English) of a number.

In mathematics, a number is divided by another number by the division method and the same division method is used in the factorization of a number. So, let’s learn the procedure of factoring a number to find the factors of a number mathematically. Three simple steps are used in the factorisation of a number.

- Write the natural number from one up to a specific number.
- Divide the number by the numbers from one up to the same number to find their corresponding quotients.
- If the quotient is a natural number or an integer, then the number that divides a number is called a factor of that number. Otherwise, it is not a factor of that number.

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

Let’s find the factors of a number $6$ to know how to find the factors of every number.

The first number in natural numbers is one. So, let’s write the numbers firstly from one to six in a row.

$1,$ $2,$ $3,$ $4,$ $5$ and $6$

Now, divide the number six by each of above numbers to find their corresponding quotient. The first number in natural numbers is one. So, let’s divide the six by one firstly.

The first natural number is one and let’s divide the number six by one to find their quotient.

$6 \div 1$

$\implies$ $6 \div 1 \,=\, \dfrac{6}{1}$

$\implies$ $\dfrac{\cancel{6}}{\cancel{1}} \,=\, 6$

$\,\,\,\therefore\,\,\,\,\,\,$ $\dfrac{6}{1} \,=\, 6$

It is evaluated that the quotient of $6$ divided by $1$ is equal to $6$ and it is a whole number, which means the number $1$ divides the number $6$ completely. So, the number $1$ is called a factor of $6$.

The second natural number is two and let’s divide the number six by two to calculate their quotient.

$6 \div 2$

$\implies$ $6 \div 2 \,=\, \dfrac{6}{2}$

$\implies$ $\dfrac{\cancel{6}}{\cancel{2}} \,=\, 3$

$\,\,\,\therefore\,\,\,\,\,\,$ $\dfrac{6}{2} \,=\, 3$

It is calculated that the quotient of $6$ divided by $2$ is equal to $3$ and the number $3$ is a whole number, which means the number $2$ divides the number $6$ completely. Hence, the number $2$ is called a factor of $6$.

The third natural number is three and let’s divide the number six by three to evaluate their quotient.

$6 \div 3$

$\implies$ $6 \div 3 \,=\, \dfrac{6}{3}$

$\implies$ $\dfrac{\cancel{6}}{\cancel{3}} \,=\, 2$

$\,\,\,\therefore\,\,\,\,\,\,$ $\dfrac{6}{3} \,=\, 2$

It is evaluated that the quotient of $6$ divided by $3$ is equal to $2$ and the number $2$ is a whole number, which means the number $3$ divides the number $6$ completely. Therefore, the number $3$ is called a factor of $6$.

The fourth natural number is four and let’s divide the number six by four to find their quotient.

$6 \div 4$

$\implies$ $6 \div 4 \,=\, \dfrac{6}{4}$

$\implies$ $\dfrac{\cancel{6}}{\cancel{4}} \,=\, \dfrac{3}{2}$

$\,\,\,\therefore\,\,\,\,\,\,$ $\dfrac{6}{4} \,=\, \dfrac{3}{2}$

It is calculated that the quotient of $6$ divided by $4$ is equal to $3$ over $2$, which is not a whole number and it is a rational number or a fraction. Similarly, the $3$ divided by $2$ is equal to $1.5$ in decimal form.

$\,\,\,\therefore\,\,\,\,\,\,$ $\dfrac{6}{4} \,=\, 1.5$

It clears the number $4$ does not divide the number $6$ completely. So, the number $4$ is not a factor of $6$.

The fifth natural number is five and let’s divide the number six by five to evaluate their quotient.

$6 \div 5$

$\implies$ $6 \div 5 \,=\, \dfrac{6}{5}$

It clears that the $6$ divided by $5$ is a fraction or a rational number and it is equal to $1.2$ in decimal number form.

$\,\,\,\therefore\,\,\,\,\,\,$ $\dfrac{6}{5} \,=\, 1.2$

It clears the number $5$ does not divide the number $6$ completely. So, the number $5$ is not a factor of $6$.

The sixth natural number is six and let’s divide the number six by itself to calculate their quotient.

$6 \div 6$

$\implies$ $6 \div 6 \,=\, \dfrac{6}{6}$

$\implies$ $\dfrac{\cancel{6}}{\cancel{6}} \,=\, 1$

$\,\,\,\therefore\,\,\,\,\,\,$ $\dfrac{6}{6} \,=\, 1$

The number $6$ divides $6$ completely. So, the number $6$ is called a factor of $6$.

The above steps have proved following two things.

- The numbers $1,$ $2,$ $3$ and $6$ divide the number $6$ completely. So, they are called the factors of $6$.
- The numbers $4$ and $5$ do not divide the number $6$ completely, So, they are not called the factors of $6$.

Thus, the factors of any number can be found easily by using above simple mathematical approach.

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