Question

Write all the factors of the following number: $15$.

Answer 1

Hint: We need to find all the factors of the number $15$.
So, we will look for the positive numbers before $16$ that will completely divide the number $15$, that is, the remainder must be $0$ after dividing $15$ by any positive divisor less than $16$.


Complete step by step solution:
We need to find the factors of the number $15$.
A factor of $15$ is a positive number that gives the remainder $0$ when the number $15$ is being divided by it.
Also, a factor of $15$ will always be less than or equal to $15$.
So, we are going to look for all the positive numbers that are less than $16$ to find out the factors of $15$.
Let us start with the smallest positive number $1$.
Now, dividing $15$ by $1$, we get:
$15 \div 1 = 15$.
Clearly, the remainder is $0$ after dividing $15$ by $1$.
Thus, the number $1$ is a factor of $15$.
Now, let us take another positive number $2$.
On dividing $15$ by $2$, we get the quotient as $7$ and remainder as $1$.
Since, the remainder does not turn out to be $0$ while dividing $15$ by $2$, therefore, $2$ is not a factor of $15$.
Now, consider the next positive number $3$.
Dividing $15$ by $3$, we get:
$15 \div 3 = 5$.
Clearly, the remainder is $0$ after dividing $15$ by $3$.
Thus, the number $3$ is a factor of $15$.
Now, let us take another positive number $4$.
On dividing $15$ by $4$, we get the quotient as $3$ and remainder as $3$.
Since, the remainder does not turn out to be $0$ while dividing $15$ by $4$, therefore, $4$ is not a factor of $15$.
Now, consider the next positive number: $5$.
Dividing $15$ by $5$, we get:
$15 \div 5 = 3$.
Clearly, the remainder is $0$ after dividing $15$ by $5$.
Thus, the number $5$ is a factor of $15$.
Now, let us take another positive number $6$.
On dividing $15$ by $6$, we get the quotient as $2$ and remainder as $3$.
Since, the remainder does not turn out to be $0$ while dividing $15$ by $6$, therefore, $6$ is not a factor of $15$.
Now, let us take another positive number, $7$.
On dividing $15$ by $7$, we get the quotient as $2$ and remainder as $1$.
Since, the remainder does not turn out to be $0$ while dividing $15$ by $7$, therefore, $7$ is not a factor of $15$.
Now, let us take another positive number, $8$.
On dividing $15$ by $8$, we get the quotient as $1$ and remainder as $7$.
Since, the remainder does not turn out to be $0$ while dividing $15$ by $8$, therefore, $8$ is not a factor of $15$.
Now, let us take another positive number, $9$.
On dividing $15$ by $9$, we get the quotient as $1$ and remainder as $6$.
Since, the remainder does not turn out to be $0$ while dividing $15$ by $9$, therefore, $9$ is not a factor of $15$.
Now, let us take another positive number $10$.
On dividing $15$ by $10$, we get the quotient as $1$ and remainder as $5$.
Since, the remainder does not turn out to be $0$ while dividing $15$ by $10$, therefore, $10$ is not a factor of $15$.
Now, let us take another positive number $11$.
On dividing $15$ by $11$, we get the quotient as $1$ and remainder as $4$.
Since, the remainder does not turn out to be $0$ while dividing $15$ by $11$, therefore, $11$ is not a factor of $15$.
Now, let us take another positive number $12$.
On dividing $15$ by $12$, we get the quotient as $1$ and remainder as $3$.
Since, the remainder does not turn out to be $0$ while dividing $15$ by $12$, therefore, $12$ is not a factor of $15$.
Now, let us take another positive number $13$.
On dividing $15$ by $13$, we get the quotient as $1$ and remainder as $2$.
Since, the remainder does not turn out to be $0$ while dividing $15$ by $13$, therefore, $13$ is not a factor of $15$.
Now, let us take another positive number $14$.
On dividing $15$ by $14$, we get the quotient as $1$ and remainder as $1$.
Since, the remainder does not turn out to be $0$ while dividing $15$ by $14$, therefore, $14$ is not a factor of $15$.
Now, consider the next positive number: $15$.
Dividing $15$ by $15$, we get:
$15 \div 15 = 1$.
Clearly, the remainder is $0$ after dividing $15$ by $15$.
Thus, the number $15$ is a factor of $15$.
Therefore, all the factors of $15$ are as follows:
$1$, $3$, $5$ and $15$.

Note:
The factors of a number can also be found using multiplication.
We just need to write the number $15$ as a product of two numbers that are less than or equal to $15$, in different ways.
The numbers involved in the products will be the factors of $15$.
The number $15$ can be written as a product of two numbers in the following possible ways:
$15 = 1 \times 15$
$15 = 3 \times 5$
Therefore, the factors of $15$ are $1$, $3$, $5$ and $15$.