Question

Write all the factors of the following numbers $\left( i \right)24\left( {ii} \right)15\left( {iii} \right)21\left( {iv} \right)27\left( v \right)12\left( {vi} \right)20\left( {vii} \right)18\left( {viii} \right)23\left( {ix} \right)36$

Answer 1

Hint: We are given a few numbers, we need to know the fact that when a number $a$ can be written as $b \times c$ , then $b$ and $c$ are factors of $a$. So we need to analyze each number and write the numbers in the form of $b \times c$ in all possible ways. From that, we can find the factors of all the numbers.

Complete step-by-step answer:
We are given few numbers and we are asked to write the factors of the numbers
Let’s begin with the first number

$\left( i \right)24$
Here the given number is $24$
Since the given number is an even number, it is divisible by $2$ , hence it can be written as $2 \times 12$
The sum of the digits of the number is $6$ , which is a multiple of $3$ , so it is divisible by $3$, hence it can also be written as $3 \times 8$
It is very well clear that that $24$ is a multiple of $4$ , so it is divisible by $4$, hence it can also be written as \[4 \times 6\]
Therefore the different ways to write the number $24$ are $2 \times 12$,$3 \times 8$ and \[4 \times 6\]
For every number, the number $1$ and itself is also a factor.
From this, we get the factors of $24$ to be $1,2,3,4,6,12,24$

$\left( {ii} \right)15$
Here the given number is $15$
Since the given number is an odd number, it is not divisible by $2$
The sum of the digits of the number is $6$ , which is a multiple of $3$ , so it is divisible by $3$, hence it can also be written as $3 \times 5$
For every number, the number $1$ and itself is also a factor.
From this, we get the factors of $15$ to be $1,3,5,15$

$\left( {iii} \right)21$
 Here the given number is $21$
Since the given number is an odd number, it is not divisible by $2$
The sum of the digits of the number is $3$ , which is a multiple of $3$ , so it is divisible by $3$, hence it can also be written as $3 \times 7$
For every number, the number $1$ and itself is also a factor.
From this, we get the factors of $21$ to be $1,3,7,21$

\[\left( {iv} \right)27\]
 Here the given number is $27$
Since the given number is an odd number, it is not divisible by $2$
The sum of the digits of the number is $9$ , which is a multiple of $3$ , so it is divisible by $3$, hence it can also be written as $3 \times 9$
For every number, the number $1$ and itself is also a factor.
From this, we get the factors of $27$ to be $1,3,9,27$

$\left( v \right)12$
 Here the given number is $12$
Since the given number is an even number, it is divisible by $2$ , hence it can be written as $2 \times 6$
The sum of the digits of the number is $3$ , which is a multiple of $3$ , so it is divisible by $3$, hence it can also be written as $3 \times 4$
Therefore, the different ways to write the number $24$ are $2 \times 6$and $3 \times 4$
For every number, the number $1$ and itself is also a factor.
From this, we get the factors of $12$ to be $1,2,3,4,6,12$

$\left( {vi} \right)20$
 Here the given number is $20$
Since the given number is an even number, it is divisible by $2$ , hence it can be written as $2 \times 10$
It is very well clear that that $20$ is a multiple of $4$ , so it is divisible by $4$, hence it can also be written as \[4 \times 5\]
Therefore, the different ways to write the number $20$ are $2 \times 10$and \[4 \times 5\]
For every number, the number $1$ and itself is also a factor.
From this, we get the factors of $20$ to be $1,2,4,5,10,20$

$\left( {vii} \right)18$
 Here the given number is $18$
Since the given number is an even number, it is divisible by $2$ , hence it can be written as $2 \times 9$
The sum of the digits of the number is $9$ , which is a multiple of $3$ , so it is divisible by $3$, hence it can also be written as $3 \times 6$
Therefore, the different ways to write the number $18$ are $2 \times 9$and $3 \times 6$
For every number, the number $1$ and itself is also a factor.
From this, we get the factors of $18$ to be $1,2,3,6,9,18$

$\left( {viii} \right)23$
 Here the given number is $23$
Since the given number is a prime number, the only factors of $23$are $1$ and $23$

$\left( {ix} \right)36$
Here the given number is $36$
Since the given number is an even number, it is divisible by $2$ , hence it can be written as $2 \times 18$
The sum of the digits of the number is $9$ , which is a multiple of $3$ , so it is divisible by $3$, hence it can also be written as $3 \times 12$
It is very well clear that that $36$ is a multiple of $4$ , so it is divisible by $4$, hence it can also be written as \[4 \times 9\]
We also know that $36$ can be written as $6 \times 6$
Therefore the different ways to write the number $36$ are $2 \times 18$,$3 \times 12$,\[4 \times 9\] and $6 \times 6$
For every number, the number $1$ and itself is also a factor.
From this, we get the factors of $36$ to be $1,2,3,4,6,9,12,18,36$

Note: While writing factors many students leave out the number one and the number itself but when all the factors are asked, we must write one and the number itself along with the other factors. Same way, for prime numbers the only factors are one and themselves, students need not confuse while writing the factors of the prime numbers.