TenMarks teaches you how to find prime factors of a number using division method.
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Learn about Prime Factorization using Division Method This track teaches us how to do prime factorization of a number by the division method. And they’ve given us two questions to do. Find the prime factorization of the following by the division method and the numbers are 12 and 480. So let’s do 12 first. So, in order to find the prime factors of 12, I simply follow one step and keep repeating it. And the step basically is that I divide the number by the least or the smallest prime number possible that leaves no remainder, it cannot leave a remainder. So let’s use this example. Let’s take 12 and let’s divide 12. What’s the smallest prime number I can divide 12. Smallest prime number is 2. So when I divide 12 by 2, I get 6. Okay? That’s step 1. Step 2, let’s divide 6 by the smallest prime number that I can find. Well, 6 can be divided by 2, so 6 divided by 2 gives me 3. Okay, now I'm left with 3, so I now divide 3 with the smallest prime number which will mark or leave a remainder. If I divide by 2, it will actually leave a remainder. So, let’s move up to dividing by three which is again a prime number. So 3 divided by 3, gives me 1. Once I reached 1, there is no more that I can divide any way because 1 cannot be divided by anything but itself. So now, I can combine these three steps and divided by 2, it gives me 6, and divide by 2 gives me 3, and divide by 3 gives me 1. I just combined these three steps, okay? The prime factorization are these numbers. The prime factorization is 2×2×3 or the prime factors is 2²×3. There are two different ways I can represent this. These are the prime factors. Let’s do the same thing for the second number which I believe is 480. I'm going to create a little bit of extra space and let’s try doing the same thing. So 480, let’s divide this by the smallest prime factor which is 2 first, right? So 480 divided by 2, gives me 240. Let’s take the next step which is 240 divided by 2 again, that gives me 120. 120 divided by 2 gives me 60, 60 divided by 2 gives me 30. I’ll keep going. 30 divided by 2 gives me 15, 15, I can no longer divide by two, so let’s get to the next prime number which is 3. 15 divided by 3 gives me 5. 5 I can no longer divide by 3 because it will leave a remainder. So the next prime number is 5, which gives me a 1. So I can combine all of these or I can simply multiply these. So the prime factors are 2×2×2×2×2×3×5, which I can also write as 25 x3×5. Okay? So to quickly recap what we’ve learned, it’s relatively easy to take a number and to compute its prime factors. In order to do that, I have to divide it by the lowest prime number possible which leaves no remained and keep doing that. So, in case of 12, I divide it by the lowest prime number which is 2 to get 6, 6 I divide again by 2 to get 3, 3 I divide again by 3 this time because I can no longer divide it by 2, and that gives me the prime factors. Similarly, if I take a larger number, like 480, we realized that first we divide it by 2, 2, 2, 2, to get 240, 120, 60, 30. I keep dividing by 2 until I get a number of 15 which can no longer be divided by this smallest prime number, so I go to the next prime number which is 3, then I go to the next prime number which is 5. And the answer, the prime factors are 2, 2, 2, 2, 2, 3 and 5, all multiplied together which can be written in exponential form as well.

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