# How do you find the prime factor of a number ?

Prime Factorization is finding the prime numbers which when multiplied together to gives the original number back

## Answer: Prime factors of a number can be found by prime factorization of the given number

We have two ways to prime factorise the numbers

- Factor tree method
- Division method

## Explanation:

### Method 1: Prime factorization using factor tree method

In the factor tree method, the factors of a number are found and then those numbers are further factorized until we reach the prime numbers. To evaluate the prime factorization of a number using the factor tree method, follow the steps given below:

**Step 1:**Consider the number as the root of the tree that is at the top of the factor tree.**Step 2:**Then write down the corresponding pair of factors as the branches of the tree.**Step 3:**Factorize the composite factors that are found in step 2, and write down the pair of factors as the next branches of the tree.**Step 4:**Repeat step 3, until we get the prime factors of all the composite factors.

Example:Find the prime factors of 225 using factor tree method

### Method 2: Division method

The division method can also be used to find the prime factors of a large number by dividing the number by prime numbers. Follow the steps given below to find the prime factors of a number by using the division method:

**Step 1:**Divide the number by the smallest prime number such that the smallest prime number should divide the number completely.**Step 2:**Again, divide the quotient of step 1 by the smallest prime number.**Step 3:**Repeat step 2, until the quotient becomes 1.**Step 4:**Finally, multiply all the prime factors that are the divisors of the division.

Example: Find the prime factors of 225 using division method