Explain what Prime Factorization is, what it represents, and how it is found. Give an example to illustrate an explanation. Make sure to explain the difference between a prime number and a composite number. (3 points)
Prime factorization is a mathematical process that involves breaking down a number into its prime factors, which are the prime numbers that can be multiplied together to produce the original number. It represents the unique combination of prime factors that make up a given number.
A prime number is a number that is only divisible by 1 and itself, such as 2, 3, 5, 7, etc. On the other hand, a composite number has more than two factors and can be divided evenly by numbers other than 1 and itself.
To find the prime factorization of a number, we start by dividing it by the smallest prime number possible. If the number is divisible by the prime number, we divide it until it is no longer divisible. Then we repeat the process with the next prime number, continuing until the number is reduced to 1.
For example, let's find the prime factorization of 36. We start by dividing 36 by 2, which gives us 18. Since 18 is also divisible by 2, we divide it again to get 9. Now, 9 is divisible by 3, so we divide it once more to get 3. Finally, as 3 is a prime number, we stop and have the prime factorization of 36, which is 2^2 * 3^2.
In this example, the number 36 is a composite number because it has more than two factors. Its prime factorization, 2^2 * 3^2, represents the unique combination of prime factors (2 and 3) that when multiplied together, give the original number 36.