Prime Factorization What is Prime factorization Prime factorization is defined as a way of finding the prime factors of a number such that the original number is evenly divisible by these factors we know that a composite number has more than two factors therefore this method is applicable only for composite numbers and not for prime numbers For example As The prime factors of 126 will be 2 3 and 7 2 3 3 7 126 So 2 3 7 are prime numbers Prime factorization Examples Prime factorization of 12 is 2 2 3 22 3 Prime factorization of 18 is 2 3 3 2 32 Prime factorization of 24 is 2 2 2 3 23 3 Prime factorization of 20 is 2 2 5 22 5 Prime factorization of 36 is 2 2 3 3 2 3 Prime Factorization Methods The most commonly used prime factorization methods are a Method b Factor Tree Method Example a Division Method for Prime Factorization 2 Below is a detailed step by step process of prime factorization by taking 460 as an example Step 1 Divide 460 by the least prime number i e 2 So 460 2 230 Step 2 Again Divide 230 with the least prime number which is again 2 Now 160 2 115 Step 3 Divide again with the least prime number which will be 5 So 115 5 23 Step 4 As 23 is a prime number divide it with itself to get 1 Now the prime factors of 460 will be 22 x 5 x 23 For example 3 Step 1 Step 2 Step 3 Step 4 4 b Tree Method To find the prime factorization of the given number using factor tree method follow the below steps Consider the given number as the root of the tree Write down the pair of factors as the branches of a tree Again factorize the composite factors and write down the factors pairs as the branches Repeat the step until to find the prime factors of all the composite factors For Example 5 6