Q: What are the factor combinations of the number 369,708?

 A:
Positive:   1 x 3697082 x 1848543 x 1232364 x 924276 x 6161812 x 30809
Negative: -1 x -369708-2 x -184854-3 x -123236-4 x -92427-6 x -61618-12 x -30809


How do I find the factor combinations of the number 369,708?

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 369,708, 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.

1 369,708
-1 -369,708

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 369,708.

Example:
1 x 369,708 = 369,708
and
-1 x -369,708 = 369,708
Notice both answers equal 369,708

With that explanation out of the way, let's continue. Next, we take the number 369,708 and divide it by 2:

369,708 ÷ 2 = 184,854

If the quotient is a whole number, then 2 and 184,854 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 2 184,854 369,708
-1 -2 -184,854 -369,708

Now, we try dividing 369,708 by 3:

369,708 ÷ 3 = 123,236

If the quotient is a whole number, then 3 and 123,236 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 3 123,236 184,854 369,708
-1 -2 -3 -123,236 -184,854 -369,708

Let's try dividing by 4:

369,708 ÷ 4 = 92,427

If the quotient is a whole number, then 4 and 92,427 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 92,427 123,236 184,854 369,708
-1 -2 -3 -4 -92,427 -123,236 -184,854 369,708
Keep dividing by the next highest number until you cannot divide anymore.

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

123461230,80961,61892,427123,236184,854369,708
-1-2-3-4-6-12-30,809-61,618-92,427-123,236-184,854-369,708

More Examples

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