Question Video: Finding the Prime Factorization of a Large Number Mathematics • 6th Grade

Find the prime factorization of 792.

03:03

Video Transcript

Find the prime factorization of 792.

We’re going to use the division method to find the prime factorization of this number. When we perform this process, we want to find all the prime numbers that multiply together to make 792. And so we list the first few prime numbers. And then the first step is to find the smallest prime number that’s also a factor of the original number. 792 is even, so we know it has a factor of two. Let’s divide then 792 by two. 792 divided by two is 396. Now, we can equivalently say that 792 is equal to two times 396.

Step two is to repeat this process with the quotient, the number we got when we performed the division. So we need to find the smallest prime factor of 396. Well, once again, it’s even, so that’s two. We’re, therefore, going to calculate 396 divided by two. That’s 198. This means 396 is equal to two times 198. And it means, in turn, we can rewrite 792 as two times two times 198.

We continue to divide our quotients by their smallest prime factor. And we only stop when our quotient is also prime. So we need to divide 198 by its smallest prime factor, which is once again two. 198 divided by two is 99. So equivalently, we can say that 198 must be equal to two times 99. We now need to divide 99 by its smallest prime factor. But 99 is not even. So it’s not divisible by two. We do, however, know that it’s divisible by three. And of course, we might recall that we can check for divisibility by three by adding the digits of the number together. If their sum is divisible by three, then the original number is also divisible by three. In this case, nine plus nine is 18. Now, 18 is divisible by three. So 99 must be divisible by three.

And in fact, when we divide 99 by three, we get 33. So we rewrite 99 is three times 33. And 792 is now two times two times two times three times 33. The smallest prime factor of 33, the smallest factor that’s also a prime number, is three. And when we divide 33 by three, we get 11. Now, 11 itself is also a prime number. It’s in our list here, so we finish dividing. We write 33 is three times 11, and this means 792 is two times two times two times three times three times 11. We can go even further and write this in exponent form. Two times two times two is two cubed and three times three is three squared. We can use a dot instead of a multiplication symbol, and we see that 792 is two cubed times three squared times 11.

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