Q: What are the factor combinations of the number 369,804?

 A:
Positive:   1 x 3698042 x 1849023 x 1232684 x 924516 x 6163412 x 30817
Negative: -1 x -369804-2 x -184902-3 x -123268-4 x -92451-6 x -61634-12 x -30817


How do I find the factor combinations of the number 369,804?

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 369,804, 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.

1 369,804
-1 -369,804

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 369,804.

Example:
1 x 369,804 = 369,804
and
-1 x -369,804 = 369,804
Notice both answers equal 369,804

With that explanation out of the way, let's continue. Next, we take the number 369,804 and divide it by 2:

369,804 ÷ 2 = 184,902

If the quotient is a whole number, then 2 and 184,902 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 2 184,902 369,804
-1 -2 -184,902 -369,804

Now, we try dividing 369,804 by 3:

369,804 ÷ 3 = 123,268

If the quotient is a whole number, then 3 and 123,268 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 3 123,268 184,902 369,804
-1 -2 -3 -123,268 -184,902 -369,804

Let's try dividing by 4:

369,804 ÷ 4 = 92,451

If the quotient is a whole number, then 4 and 92,451 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 92,451 123,268 184,902 369,804
-1 -2 -3 -4 -92,451 -123,268 -184,902 369,804
Keep dividing by the next highest number until you cannot divide anymore.

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

123461230,81761,63492,451123,268184,902369,804
-1-2-3-4-6-12-30,817-61,634-92,451-123,268-184,902-369,804

More Examples

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