Factoring Integers
Step-by-Step Integer Factorization
Step 1: Start with a Number
Let's begin by choosing a number to factor:
Step 2: Find the Smallest Factor
What's the smallest number that divides into this number evenly?
Steps taken:
Quiz Mode
Enter the prime factorization (use x as multiplication symbol):
How to Factor Integers
Factoring integers is the easiest thing we can factor. It means to make the integer look like a multiplication problem by looking for its prime factorization. In other words, factor the integer until all factors are prime numbers.
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It is very important to know how to do this before learning how to find the greatest common factor and how to factor trinomials.
Here is the algorithm:
When factoring, start by dividing the number by 2. Then, keep dividing any factor divisible by 2 that is not prime by 2 until no factors are divisible by 2.
When no factors are divisible by 2, start by dividing by 3 until no factors are
divisible by 3.
When no factors are divisible by 3, start by dividing by 4 until.....
and so forth...
Factoring Integers with a Couple of Example.
Example #1
Factor 4
Dividing 4 by 2 gives 2, so
4 = 2 * 2
Example #2
Factor 12
Dividing 12 by 2 gives 6, so
12 = 2 * 6
However, 6 is a factor divisible by 2, so factor 6.
Factoring 6 gives 2 * 3
Putting it all together,
12 = 2 * 6 = 2 * 2 * 3
When factoring integers a problem can get complicated when the number is big. when this happens make a tree as the following example demonstrates. We call this a factor tree.
Factor 72
Pulling out all factors inside the red shape that looks like a golf bat, we get:
72 = 2 * 2 * 2 * 3 * 3
Example #4
Factor 240
Once again, pulling out all factors inside the red shape that looks like a golf bat, we get:
240 = 2 * 2 * 2 * 2 * 3 * 5
You should notice tough that 72 and 240 can be factored faster than that if you know very well your multiplication table.
72 = 8 * 9
8 = 2 * 2 * 2 and 9 = 3 * 3
So, 72 = 2 * 2 * 2 * 3 * 3
240 = 24 * 10
10 = 2 * 5 and 24 = 4 * 6 = 2 * 2 * 2 * 3
So, 240 = 2 * 2 * 2 * 2 * 3 * 5