Question

How do you write $18$ as the product of prime factors?

Answer 1

Prime factorization is a way to write a composite number as the product of prime factors. Prime factors are those numbers or factors which are greater than $1$ and have exactly two factors, $1$ and itself. There are basically two ways to find prime factorization and that are
a) by division method
b) by factor tree
Here, in this question let us try to show $18$ as the product of prime factors by division method.

Complete step by step solution:
We know that the number $2$ is the smallest prime number. So, in order to find prime factors of $18$ let us first divide $18$ by the least prime number that is $2$.
$18 \div 2 = 9$
Now, we know that $9$ is not divisible by $2$ so we move to the next prime number known to us, which is $3$. So, we divide $9$ by $3$.
$9 \div 3 = 3$
Now, again we got $3$ as a quotient so we divide $3$ by $3$ because we cannot divide $3$ by the least prime number that is $2$. We will continue this process of dividing until and unless we get quotient as $1$.
$3 \div 3 = 1$
As now we got $1$ as quotient, we can say that the prime factors of $18$ are $2,3,3$.
In mathematical terms the prime factorization of $18 = 2 \times 3 \times 3 = 2 \times {3^{^2}}$.

Note: Here is another way of calculating prime factors of number $18$, which is by factor tree. Under this way, we keep on splitting the number into its prime factors. It will be clearer through the following diagram of the factor tree.
Above is the factor tree of $18$. The factors of $18$ are $2,3,3$.
The prime factorization of $18$ can be written as $18 = 2 \times 3 \times 3 = 2 \times {3^{^2}}$.