What Are Relative Prime Numbers in Math?

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Relative prime numbers, in mathematics terms, are numbers that have a few very clear characteristics. Learn about relative prime numbers in math with help from a longtime mathematics educator in this free video clip.

Part of the Video Series: Number Theory Education
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Video Transcript

Hi, I'm Jimmy Chang, and we're here to answer the question, what are relative prime numbers in math? Now, two numbers are relatively prime if they have no common positive factors besides one. So, in other words, the two numbers or three numbers, if you want to consider that, as well, the numbers themselves may not have to be prime, but the only factors they have in common would just be one. So, for example, if you have the numbers twelve and twenty-five, the factors of twelve are one, two, three, four, six, and twelve, but the factors of twenty-five are one, five, and twenty-five. Now, the only factors that they have in common is going to be one, because they don't share anything else. That makes these two numbers relatively prime. That fits the definition, because they don't have any common positive factors besides the number one itself. Now, it really depends on what numbers that you're comparing, but these are examples of relatively prime. But, if you have the number six and the number, let's just say fifteen, the factors of six are one, two, three, and six, and the factors of fifteen are one, three, five, and fifteen. This is an example of two numbers that are not relatively prime, because, yes, they have the number one in common as a factor. But, if you notice, they also have the number three in common as a factor. So, this is an example of two numbers that are not relatively prime. So, numbers can only be relatively prime if the only factors that they share is just the number one. So, I'm Jimmy Chang, and that answers the question, what are relative prime numbers in math?


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