How to Find a Number as a Product of Primes

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Finding a number as a product of primes is also commonly referred to as prime factorization. Find a number as a product of primes 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 talk about how to find a number as a product of primes. Now, when you're doing that, you're pretty much doing what we call a prime factorization, because the idea is you can take any number and write it as a product of primes, and that's using the prime factorization theory, if you will. So, for example, if you just take the number twelve--any number will do--what you want to do is you break up the number twelve into as much as you can, into as small as numbers as possible. And these numbers will be the primes themselves. So, now, you take twelve, for example, and just break it up any way want. It can be three times four, six times two, etcetera. So, let's just do four times three. And, understand that because three is a prime, three cannot be broken up any further. So, you leave the three as is, but anytime you have a prime, you just circle it for tracking. Now, the four, though, can be broken down further. So, four can be broken up into two times two. Now, as you already know, twos cannot be broken down any further, because they're prime. So, we're going to circle those individually. Now, that means twelve is broken up as two times two times three. So, any number, as long as you do what we call a factorization tree and broken up into primes, you're pretty much done, and the problem is complete. So, twelve can be rewritten as two times two times three. As you can tell, it's a product of primes, but you will always get to this kind of result if you use the prime factorization. So, I'm Jimmy Chang, and that's how to write a number as a product of primes.


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