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**Hint:**We solve this problem from the definition of factor. The factor of a number \['x'\] is defined as a number which is less than or equal to \['x'\] which divides the number \['x'\] exactly which means the remainder is zero. We take all numbers less than or equal to 6 and divide 6 with all numbers and check the numbers which are factors of 6.

**Complete step-by-step answer:**

We are asked to find the all the factors of 6

We know that the factor of a number \['x'\] is defined as a number which is less than or equal to \['x'\] which divides the number \['x'\] exactly which means the remainder is zero.

Let us take all the numbers less than or equal to 6 and divide the number 6 with all those numbers

(i) Let us check for 1

By dividing the number 6 with 1 we get

\[\Rightarrow \dfrac{6}{1}=6\]

Here, we can see that the remainder is zero

So, we can say that the number 1 is factor of 6

(ii) Let us check for 2

By dividing the number 6 with 2 we get

\[\Rightarrow \dfrac{6}{2}=3\]

Here, we can see that the remainder is zero

So, we can say that the number 2 is factor of 6

(iii) Let us check for 3

By dividing the number 6 with 3 we get

\[\Rightarrow \dfrac{6}{3}=2\]

Here, we can see that the remainder is zero

So, we can say that the number 3 is factor of 6

(iv) Let us check for 4

By dividing the number 6 with 4 we get

\[\Rightarrow \dfrac{6}{4}=1.5\]

Here, we can see that the remainder is not zero because the result is in decimal

So, we can say that the number 4 is not a factor of 6

(v) Let us check for 5

By dividing the number 6 with 5 we get

\[\Rightarrow \dfrac{6}{5}=1.2\]

Here, we can see that the remainder is not zero because the result is in decimal

So, we can say that the number 5 is not a factor of 6

(vi) Let us check for 6

By dividing the number 6 with 6 we get

\[\Rightarrow \dfrac{6}{6}=1\]

Here, we can see that the remainder is zero

So, we can say that the number 6 is factor of 6

Therefore the factors of 6 are 1, 2, 3, 6.

So, option (d) is the correct answer.

**So, the correct answer is “Option (d)”.**

**Note:**We have a short cut of this solution that is writing all the possible pairs of numbers such that the product is 6 that is

\[\begin{align}

& \Rightarrow 6=1\times 6 \\

& \Rightarrow 6=2\times 3 \\

\end{align}\]

Here, there are four numbers whose selected product results 6

So, the factors of 6 are 1, 2, 3, 6.

So, option (d) is the correct answer.

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