Question

Write down all the factors of \[36\].

Answer 1

Hint:First of all, we have to check and find the numbers that divide the given number with the remainder zero. Those are called factors. Here we have to find the factors of \[36\].

Complete step-by-step answer:
We can define a factor as a number that is multiplied to get another number. The same number may repeat in the process. But we have to consider it as only one factor. Mostly numbers have an even number of factors. But a square number has an odd number of factors and a prime number has only two factors – one and the number itself.
For example,
\[ \Rightarrow 2 \times 3 = 6\]
In the above example, \[2\] and \[3\] are called the factors of \[6\].
\[6\] can also be written as,
\[ \Rightarrow 6 \times 1 = 6\]
Therefore, \[6\]and \[1\] are also called the factors of \[6\].
So, for the above question, we have to write all the possible factors.
\[36\] can be written as,
\[ \Rightarrow 1 \times 36 = 36\]
\[ \Rightarrow 2 \times 18 = 36\]
\[ \Rightarrow 3 \times 12 = 36\]
\[ \Rightarrow 4 \times 9 = 36\]
\[ \Rightarrow 6 \times 6 = 36\]
The factors of \[36\] in all possible ways:
\[1,{\text{ }}2,{\text{ }}3,{\text{ }}4,{\text{ }}6,{\text{ }}9,{\text{ }}12,{\text{ }}18,{\text{ }}36\]
These are the positive factors of \[36\].

Note: The best way to find the factors of any number is to divide it by the smallest prime number that goes into it evenly with no remainder. Continue this process with each number you get, until you reach 1.
There is a process called prime factorization. With that process we can find the number of factors, the product of factors, the sum of factors, and also factors to some extent.
The formula for the number of factors of \[N\] according to the prime factorization process,
\[N = ({\text{a + 1)(b + 1)(c + 1)}}\].