Using prime factorization to find the GCF
- List the prime factors of each number.
- Circle every common prime factor — that is, every prime factor that’s a factor of every number in the set.
- Multiply all the circled numbers. The result is the GCF.
What is the prime factorization tree of 875?
Results: The number 875 is a composite number because 875 can be divided by 1, by itself and at least by 5 and 7. So, it is possible to draw its prime tree. The prime factorization of 875 = 53•7.
How to do a factor tree with prime numbers?
Break down your first two factors into their own sets of two factors apiece. As before, two numbers can only be considered factors if they equal the current value when multiplied together. Do not break down prime numbers any further. …../…\ ………/ \ Repeat until you reach nothing but prime numbers.
How to think about the prime factorization of a number?
One way to think about solving for the prime factorization of a number is to think about leaves on a tree. The tree is the given number. As we break it down, we create branches, and when we get to the smallest factors, we see the leaves. The connection to trees isn’t an accident.
What do you need to know about making a factor tree?
The process required for making a factor tree is the same as described in the “Making a Factor Tree” section. The GCF between two or more numbers is the largest prime number factor that is shared between all of the given numbers in the problem. This number must divide evenly into all of the original numbers in the problem.
Which is the first branch of a factor tree?
To qualify as a pair of factors, the product of the two numbers must equal your original number when multiplied together. These factors will form the first branches of your factor tree. You can pick any two factors. The end result will be the same no matter which ones you start with.
