This week I learned about two different types of prime factorization techniques, division tables and factor trees. A prime factor is a number that is only divisible by 1 and itself.

Division Table

When using a division table you must start with finding the smallest possible prime factor of your number. After the prime factor has been found you must then divide the number by the prime factor. Repeat those steps until you find the lowest possible prime factors of your equation.

Because the number 7575 ends in a 5 I will divide 7575 by 5 as 5 is the lowest prime number that 7575 is able to be divided into. I’m left with the number 1515, this number ends in 5 so I will divide it by five as well. This leaves me with 303, if I add the sum of 303 together I’m left with 6, because the number 3 is able to fit in the number 6 I will divide 303 by 3. The number I am left with is 101, because 101 is a prime number I no longer need to divide anything. Now I will times all my prime numbers by each other, leaving me with the equation, .

Because the number 120 is an even number I will divide it by 2. After I have divided the number 120 by 2 I’m left with the number 60. 60 is an even number as well so I’m going to divide by 2 again. This leaves me with the number 30, so I will divide by 2 again as 30 is an even number. I now have the number 15, if I add the sum of 15 together it leaves me with 6, because the number 3 is divisible by 3 I am able to divide 15 by 3. I am left with the prime number 5. I then multiply all the numbers together, .

 

Factor Tree

For a factor tree you start by writing your number and a ^ sign (branch) underneath it. Underneath each side of the ^ you write a factor pair (a set of factors that are equivalent to the particular number you are working with). You then continue these steps until each “branch” ends in a prime factor. When creating a factor tree it does not matter if you start with the lowest prime number possible or not.

Because the number 7575 ends in a 5 I will divide 7575 by 5 as 5 is the lowest prime number that 7575 is able to be divided into. I’m left with the number 1515, this number ends in 5 so I will divide it by five as well. This leaves me with 303, if I add the sum of 303 together I’m left with 6, because the number 3 is able to fit in the number 6 I will divide 303 by 3. The number I am left with is 101, because 101 is a prime number I no longer need to divide anything. Now I will times all my prime numbers by each other, leaving me with the equation, .

 

Because the number 120 ends in a 0 I will divide it by 5. After I have divided the number 120 by 5 I’m left with the number 24. 24 is an even number as well so I’m going to divide by 2. This leaves me with the number 12, so I will divide by 2 again as 12 is an even number. I now have the number 6, because the number 6 is divisible by 3 I am able to divide 6 by 3. I am left with the prime number 2. I then multiply all the numbers together, .

 

Why I chose this topic

I chose to do this topic as I find it important to be able to show my work and these methods allow me to demonstrate how I found the prime factors of a number. I also like having options to choose between when doing math, and I wanted to share that both of these methods are effective and produce the same answer.