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Factorizing Large Numbers

FactorizingIn an earlier blog post, we talked about what prime factorization is and how to use a factor tree to factor numbers to their prime factors.


What if the number you are finding the prime factorization of is a larger number? The factor tree can become quite cumbersome.

Using upside-down division

Another easy way of keeping track of the factorization is to do upside-down division.


Here’s how it works. Let’s start with a smaller number first – say 36.

 

 

 

 

You start by dividing 36 by 2.

Factorizing
 

 

 

 

36 divided by 2 is 18.

factorizing
 

 

 

 

 

Then you divide 18 by 2.

Factorizing
 

 

 

 

 

 

18 divided by 2 is 9.

Factorizing
 

 

 

 

 

 

 

9 divided by 2 does not make a whole number, but divided by 3 it does.

Factorizing
 

 

 

 

 

 

 

 

 

9 divided by 3 is 3.


When completed, the prime factorization is the product of all the numbers around the outside.

Factorizing
 

 

 

 

 

 

 

 

 

 

2 x 2 x 3 x 3 = 36

Factorizing Larger Numbers

Now, when you try the upside-down division with a larger number, you’ll see how easy this method is.

Factorizing
 

 

 

 

 

 

 

 

 

 

 

 

The answer is: 2 x 3 x 5 x 5 x 7 = 1050.