This week in math, we did some review with integers as well as linear equations. After refreshing our minds on how to solve equations correctly we moved on to prime factorization. With prime factorization we learned how to figure out the prime numbers in any number with the help of factor trees and division tables.
Lets say we have the number 1911 and we want to express the prime factorization of this number. Since this is a big number we will try a division table. We will first start off with figuring out what the factors of this number are. By adding all of the digits in this equation and dividing it by 3 is how I figured out you can divide this number by 3.
The next step is to figure out what 3 divided by 1911 is. In order to do this in a quick and easy way we will need to put 3 into each number within this number. For example we start off with 3 going into 1. Obviously we know we cant put 3 into 1 so what we are going to do is move up a digit. Instead of doing 3 into 1 we will do 3 into 19. Of course 3 doesn’t perfectly go into 19 but it does go in 6 times. 6 multiplied by 3 is 18 which leave us with a remainder of 1, since our number was 19. So, we can’t just leave this number with the 1 hanging around, we have to put the 1 somewhere. We are going to move it up and make the next number (which is 1) a double digit number, 11. I put the 1 we moved, in red so we know that is how we got 11. All we have to do is continue this process. 3 goes into 11, 3 times with a remainder of 2. We move that 2 up to make the 1 a 21. 3 then goes into 21 exactly 7 times which leaves us with our number 637. You continue to do this process with 637, figuring out first what its divisible by and then putting that number into each number.
Our final step is to make sure we have our final number. In order to do that we just make sure that our number is a prime number. A prime number is one that is only divisible by 1 and itself. As you can see we have 13 and 13 is a prime number so we know that it’s our final. All we have left is to put all of the prime factors in order from least to greatest. When we have multiple of the same prime factor, like the two 7’s we have, we can use exponents to show that there are multiple. We use the dot in between each number to show multiplication because using X can confuse us.
