# Topic 3

# What is Prime Factorization and when will we need to use it

## What does Prime Factorization even mean?

Prime Factorization means what lowest prime number can be multiplied to make the base or original number.

## When do we use Prime Factorization?

We use Prime Factorization for questions like find the square root of 64 and to see if a number is a perfect square.

## How do we do prime factorization? Lets take the square root of 64.

For this we will find the lowest prime number that can divide 64 . So it will be like this 64/2 = 32. Then we will divide that number by the lowest prime number. 32/2 =16 . After that we will divide that number by lowest prime number and we get 8. Then we will divide that by lowest prime number and get 4. After we will divide 4/ 2 and we get 2. Then we will list the divisors . 2, 2,2,2,2,2. After that we will make 2 groups and multiply them meaning, (2x2x2) (2x2x2) meaning the square root is 8.

## When will we use Prime Factorization in real life?

We never know when we will have to use prime factorization in real life. It may be used for anything. We might have already used it but we don't even remember. An example is how will you solve 5904/24 for dividing equally? You will divide bot numbers by the same prime factors. Like this 5904 /2 and 24 / 2. That will be equal to 2952/1 2. Then we can simplify it farther like this 2952 / 2 and 12/2 = 1476 / 6. We can then divide it by 2 again. 1476/2 and 6/2 which is 738/3. We can then divide that by 3 like this 738/3 = 246. We just solved a very big number divided by a big number mentally using prime factorization!

## Whats the method to do prime factorization?

OK so lets assume a variable called A. Then lets divide this number by the lowest prime number it can divide from . After that lets keep doing this until the number is not dividable by any prime numbers any more. Then we put prime factors in a row of what we divided each number by in multipication way. EX, 2x2x3x3x2x2.

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