Factoring 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.

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...

Let us start practicing 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.

Example #3

Factor 72
Factor tree of 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

Factor tree of 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

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