Q: What are the factor combinations of the number 130,812?

 A:
Positive:   1 x 1308122 x 654063 x 436044 x 327036 x 2180211 x 1189212 x 1090122 x 594633 x 396444 x 297366 x 1982132 x 991
Negative: -1 x -130812-2 x -65406-3 x -43604-4 x -32703-6 x -21802-11 x -11892-12 x -10901-22 x -5946-33 x -3964-44 x -2973-66 x -1982-132 x -991


How do I find the factor combinations of the number 130,812?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 130,812, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 130,812
-1 -130,812

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 130,812.

Example:
1 x 130,812 = 130,812
and
-1 x -130,812 = 130,812
Notice both answers equal 130,812

With that explanation out of the way, let's continue. Next, we take the number 130,812 and divide it by 2:

130,812 ÷ 2 = 65,406

If the quotient is a whole number, then 2 and 65,406 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 65,406 130,812
-1 -2 -65,406 -130,812

Now, we try dividing 130,812 by 3:

130,812 ÷ 3 = 43,604

If the quotient is a whole number, then 3 and 43,604 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 43,604 65,406 130,812
-1 -2 -3 -43,604 -65,406 -130,812

Let's try dividing by 4:

130,812 ÷ 4 = 32,703

If the quotient is a whole number, then 4 and 32,703 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 32,703 43,604 65,406 130,812
-1 -2 -3 -4 -32,703 -43,604 -65,406 130,812
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

123461112223344661329911,9822,9733,9645,94610,90111,89221,80232,70343,60465,406130,812
-1-2-3-4-6-11-12-22-33-44-66-132-991-1,982-2,973-3,964-5,946-10,901-11,892-21,802-32,703-43,604-65,406-130,812

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