### Theory:

Prime factorization is to write the composite number as a product of its prime factors.
Let us find the prime factor for $$12$$.

$$12 = 4 \times 3$$

$$4$$ can be written as $$2 \times 2$$.

$$12 = 2 \times 2 \times 3$$

Therefore, the prime factor of $$12$$ is $$2 \times 2 \times 3$$.
There are two ways to find the prime factor.

1. Factor tree method

2. Division method
Factor tree method
Let's see the example using factor tree method.
Example:
Find the prime factor of $$48$$ using the factor tree method. Prime factor of $$48$$ $$=$$ $$8 \times 6$$.

Prime factor of $$8$$ $$=$$ $$4 \times 2 = 2 \times 2 \times 2$$.

Prime factor of $$6$$ $$=$$ $$3 \times 2$$.

The ending prime numbers are the prime factors.

Therefore, the prime factor of $$48$$ $$=$$ $$2 \times 2 \times 2 \times 2 \times 3$$.
Division method:
Step 1: Write the given number.

Step 2: Start with the lowest prime number, which exactly divides the given number.

Step 3: Write that lowest prime number on the left side of the given number.

Step 4: Write down the quotients in the next line of the given number.

Step 5: Repeat the process until you get $$1$$ as a quotient.

Step 6: The prime numbers you obtained on the left side of the given number is prime factors.
Example:
Find the prime factor of $$27$$ using division method.

Write a pair of factors.

$$27 = 9 \times 3$$

Now further factorize the composite factor $$9$$ as $$3$$ and $$3$$.

Repeat the process till you get the prime factors of all the composite factors.

Since the last number $$3$$ is a prime number, we cannot factorize it further. Therefore, the prime factor of $$27$$ $$=$$ $$3 \times 3 \times 3$$.