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 factor 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 is 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!

Factor 4

Dividing 4 by 2 gives 2, so

4 = 2 * 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

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

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 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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