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52 as a Product of Prime Factors: Steps & How-to

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  • 0:00 Important Definitions
  • 0:50 Steps to Solving the Problem
  • 2:07 Solution
  • 2:29 Check Your Work
  • 3:29 Know Your Prime Numbers
  • 4:29 Lesson Summary
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Lesson Transcript
Instructor: Sharon Linde

Sharon has a Masters of Science in Mathematics

What are factors of a number? What are prime factors of a number and how do you find them? This lesson goes over the process of finding the prime factors of a number, using 52 as an example.

Important Definitions

How do you factor the number 52 into all of its prime factors?

Before you learn how to do this, it is important to go over some definitions. Factors are whole numbers that divide evenly into the number you are trying to factor. In this case, the number that you are trying to factor is 52. Prime numbers are numbers that have exactly 2 factors: 1 and itself. Prime factors are factors that are also prime numbers. The first six prime numbers are 2, 3, 5, 7, 11, and 13. Now that all of the definitions are out of the way, it is time to figure out the prime factors of 52.

Steps to Solving the Problem

Step 1: Find any factor of 52, besides 1 and 52

The first thing you should notice about 52 when you are trying to get its prime factors is that it ends in an even number, which means it is evenly divisible by 2. 2 is also a prime number, so 2 will end up being a prime factor of 52.

Step 2: Divide 52 by the factor you found to get another factor

To get another factor of 52, simply divide 52 by 2.

52 / 2 = 26

So, 52 = 2 x 26

Step 3: Repeat steps 1 and 2 until all of the factors are prime

Again, you should notice that 26 is not a prime factor, since it is also an even number and also evenly divisible by 2.

26 / 2 = 13

So you can use that in our equation to get that 52 = 2 x 2 x 13. Now, you have three factors of 52, all of which are prime. You're almost finished.

Solution

You factored 52 and came up with 3 factors, all of which were prime: You have 52 = 2 x 2 x 13. While this is technically three prime factors, one of them is repeated. So, 52 has two prime factors, which are 2 and 13.

Check Your Work

To see if you've gotten all the prime factors of 52, check your work. Multiply all of the prime factors you obtained for your answer together. So you have 2 x 13 = 26. If this was 52, you would be done. Since you're not quite to 52, you need to continue.

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