# CLASS-6PRIME 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:

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.
3. Move on to the next prime number, which is 3, and repeat the division process.
4. Continue this process with each successive prime number until the quotient becomes 1.
5. 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:-

2. 72 ÷ 2 = 36. Write down the factor 2.
3. 36 ÷ 2 = 18. Write down the factor 2.
4. 18 ÷ 2 = 9. Write down the factor 2 again.
5.  9 ÷ 3 = 3. Write down the factor 3.
6.  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:-

2. 60 ÷ 2 = 30. Write down the factor 2.
3. 30 ÷ 2 = 15. Write down the factor 2.
4. 15 ÷ 3 = 5. Write down the factor 3.
5. 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:-