Prime factoring a number involves breaking a number into its prime factors. Therefore to find any prime factorization of a number we will break it into its factor one by one, starting from the least possible factor that the given number could have.

**The most commonly used method nowadays is the Factor Tree Method, which is explained below:**

Consider the number 36, and we can make 36 as 2 times 18, which is equal to 36. Now we got two factors namely 2 and 18, out of which we can not break 2 into some other prime factor, and hence, we got 2 as one of the factors of 36. Now, we can break 18 a little further by breaking it into 2 times 9, and again we got another factor 2. Now 9, can again be factorized as 3 times 3, which are last factors, as 3 can not be reduced to other factors. Therefore, by combing all the factors, we get, 36 = 2 x 2 x 3 x 3, which is the prime factorization of the number 36, as 36 has been expressed as the product of prime numbers involving 2 and 3.

**This method is known as the factor tree method in which we write all the factors of a number in a tree format, circling all the prime numbers in the end which can be drawn as shown below:**

Similarly, by using the factor tree method we can find the prime factors of 1092 = 2 x 3 x 2 x 7 x 13, as shown below:

In a similar manner we can find the prime factors of a given number by repeated division method in which we divide the number again and again till all the factors involved become prime factors.

**Consider the prime factorization of 24 done by division method as shown below:** Thus, we found that 24 = 2 x 2 x 2 x 3. Hence, we got all the prime factors of 24.

**The following are some examples of how to find prime factorization of a given number:****1). **39 = 3 x 13. Note that there are only two prime factors of 39, both of which are prime numbers.

**2). **62 = 2 x 31. Note that there are only two prime factors of 62, one is 31, which is a prime number and the other is a 2, which is also a prime factor but 2 is an even number.

**3). **64 = 2 x 2 x 2 x 2 x 2 x 2. Note that there are 6 prime factors; all are equal to 2, which is an even number.

**4). **35 = 5 x 7. Note that there are only two prime factors of 35, both of which are prime number 5 and 7.

**5). **22 = 2 x 11 . Note that there are only two prime factors of 22, both of which are prime numbers.

**6). **32 = 2 x 2 x 2 x 2 x 2. Note that there are 5 prime factors; all are equal to 2, which is an even prime number.