Finding the Prime Factorization with Exponents

Finding the Prime Factorization with Exponents
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  • 0:04 Prime Numbers
  • 1:03 Factors
  • 1:32 Prime Factorization
  • 3:22 Adding Exponents
  • 3:59 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will be able to factor any number using just prime numbers and exponents. Learn how to break apart any number you are given. Then, test your new knowledge with some examples.

Prime Numbers

In this video lesson, we will learn how to break apart numbers. Yes, we can actually break apart numbers into even smaller numbers. These smaller numbers are called prime numbers. These are numbers that can only be divided evenly by 1 or itself. For example, the numbers 2 and 3 are prime numbers because you can only divide each of them by 1 and by itself. If you divide them by any other number, you will get a decimal.

You can also think of these prime numbers as numbers of items, such as candies that you are trying to divide into equal groups. Our first few prime numbers are 2, 3, 5, 7, 11, 13 and 17. We can break down numbers into smaller prime numbers. But, if we already have a prime number, then we won't be able to break that number down. It is already as broken down as we can get.

Factors

When we combine two prime numbers and multiply them to get another number, the prime numbers are also called factors, numbers that multiply together to get another number. Actually, any numbers that are multiplied with other numbers are called factors. For example, the numbers 2 and 3 in 2 * 3 are called factors because they are being multiplied together. In this example, 2 and 3 also happen to be prime numbers.

Prime Factorization

What is 2 * 3? It is 6. So, we can say that 6 can be broken down to 2 * 3. We call this process prime factorization, the breaking down of a number into the prime numbers that multiply to the original number. For example, the prime factorization of 6 is 2 * 3. Once we reach 2 * 3, we can't go any further because they are both prime numbers.

Let's look at an example. What are the prime factors of 12?

Using prime factorization, we will begin by dividing our number by the smallest prime factor that we can. In this case, it is 2. So, we divide 12 by 2; we get 6. Can 6 be broken down further? Yes, it can. We can also divide 6 by 2; we get 3. So, our 12 now looks like this 12 = 2 * 2 * 3. All of these numbers are now prime, so we are done. We can say the prime factorization of 12 is 2 * 2 * 3.

This process is kind of like taking apart something like a watch into all its little components. Once we reach the gears of the watch, we are done since we can't break apart the gears any further.

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