LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

PRIME FACTORIZATION

__PRIME FACTORIZATION -__

**Prime factorization is a process of expressing a positive integer as a product of its prime factors. Prime factors are the prime numbers that divide the given integer without leaving any remainder.**

**Here's how you can find the prime factorization of a number:**

**Start with the smallest prime number, which is 2.****Divide the given number by 2. If it's divisible, write down the factor 2 and continue dividing the result by 2 until you can no longer divide evenly.****Move on to the next prime number, which is 3, and repeat the division process.****Continue this process with each successive prime number until the quotient becomes 1.****Write down all the prime factors that you found in**__step.2__to__step.4__.

**For example, let's find the prime factorization of the number 72:-**

**Start with the smallest prime, 2.****72 ÷ 2 = 36. Write down the factor 2.****36 ÷ 2 = 18. Write down the factor 2.****18 ÷ 2 = 9. Write down the factor 2 again.****9 ÷ 3 = 3. Write down the factor 3.****3 ÷ 3 = 1. Write down the factor 3.**

**So, the prime factorization of 72 is 2^3 × 3^2, which means 72 can be expressed as the product of 2 raised to the power of 3 and 3 raised to the power of 2.**

**For example, let's find the prime factorization of the number 60:-**

**Start with the smallest prime, 2.****60 ÷ 2 = 30. Write down the factor 2.****30 ÷ 2 = 15. Write down the factor 2.****15 ÷ 3 = 5. Write down the factor 3.****5 ÷ 5 = 1. Write down the factor 5.**

**So, the prime factorization of 60 is 2^2 × 3 × 5, which means 60 can be expressed as the product of 2 raised to the power of 2, 3 raised to the power of 1, and 5 raised to the power of 1.**

**Another example: Let's find the prime factorization of 126:-**

**Start with the smallest prime, 2.****126 ÷ 2 = 63. Write down the factor 2.****63 ÷ 3 = 21. Write down the factor 3.****21 ÷ 3 = 7. Write down the factor 3.****7 is a prime number, so write it down.**

**The prime factorization of 126 is 2 × 3^2 × 7.**

**Prime factorization is useful in various mathematical contexts, such as simplifying fractions, finding the greatest common divisor (GCD), and solving certain types of equations.**