Question

All the factors of 6 are
(a) 1, 6
(b) 2, 3
(c) 1, 2, 3
(d) 1, 2, 3, 6

Answer 1

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.