Question

Write all the factors of the following number: 18.

Answer 1

Hint: In this question we will simply use the following approach, we will just divide the number by each of the counting numbers, in order until the quotient is smaller than the divisor. If the quotient is a counting number, the divisor and quotient are a pair of factors. If the quotient is not a counting number, the divisor is not a factor. List all the factor pairs. Write all the factors in order from smallest to largest.

Complete step-by-step answer:
Given number
18
Now we have to find all the factors of this number.
Let the divisor be D, quotient be Q and the remainder be R
$ \Rightarrow \dfrac{{18}}{D} = Q\dfrac{R}{D}$
Iteration – 1: when the divisor is 1
$ \Rightarrow \dfrac{{18}}{1} = 18\dfrac{0}{1}$
Here Quotient = 18 and Remainder = 0
Since, quotient must be greater than equal to the divisor, quotient should be a whole number or we can say that remainder should be equal to 0 and that condition is fulfilled here, so factor pair for the first iteration is 1,18
Iteration – 2: when the divisor is 2
$ \Rightarrow \dfrac{{18}}{2} = 9\dfrac{0}{2}$
Here Quotient = 9 and Remainder = 0
Since, quotient must be greater than equal to the divisor, quotient should be a whole number or we can say that remainder should be equal to 0 and that condition is fulfilled here, so the factor pair for the second iteration is 2,9.
Iteration – 3: when the divisor is 3
$ \Rightarrow \dfrac{{18}}{3} = 6\dfrac{0}{3}$
Here Quotient = 6 and Remainder = 0
Since, quotient must be greater than equal to the divisor, quotient should be a whole number or we can say that remainder should be equal to 0 and that condition is fulfilled here, so the factor pair for the third iteration is 3,6.
Iteration – 4: when the divisor is 4
$ \Rightarrow \dfrac{{18}}{4} = 4\dfrac{2}{4}$
Here Quotient = 9 and Remainder = 0
Since, quotient must be greater than equal to the divisor, quotient should be a whole number or we can say that remainder should be equal to 0 and that condition is not fulfilled here, so (4, 4) is not a factor.
Iteration – 5: when the divisor is 5
$ \Rightarrow \dfrac{{18}}{5} = 3\dfrac{3}{5}$
Here Quotient = 9 and Remainder = 0
Since, quotient must be greater than equal to the divisor, quotient should be a whole number or we can say that remainder should be equal to 0 and that condition is not fulfilled here, so (5, 3) is not a factor.
We stop the iterations here, because now the quotient is getting smaller than the divisor.
Factor pairs so found are (1, 18), (2, 9) and (3, 6)
So, the factors of 18 are 1, 2, 3, 6, 9 and 18
In total there are six factors including 1 and 18.
$\therefore $ The factors of 18 are 1, 2, 3, 6, 9 and 18.
So this is the required answer.

Note: For such types of questions, just keep on dividing the number starting from 1, on dividing if we get a quotient smaller than divisor stop on that iteration and list all the pairs to get the total factors of the number. Another way to cross check whether all the factors are found or not is just by writing the prime factorization of the number and finding all the possible combinations on multiplying prime factors to get all the factors of the number.