Q: What are the factor combinations of the number 928,109?

 A:
Positive:   1 x 9281097 x 13258713 x 7139331 x 2993947 x 1974749 x 1894191 x 10199217 x 4277329 x 2821403 x 2303611 x 1519637 x 1457
Negative: -1 x -928109-7 x -132587-13 x -71393-31 x -29939-47 x -19747-49 x -18941-91 x -10199-217 x -4277-329 x -2821-403 x -2303-611 x -1519-637 x -1457


How do I find the factor combinations of the number 928,109?

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 928,109, 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.

1 928,109
-1 -928,109

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 928,109.

Example:
1 x 928,109 = 928,109
and
-1 x -928,109 = 928,109
Notice both answers equal 928,109

With that explanation out of the way, let's continue. Next, we take the number 928,109 and divide it by 2:

928,109 ÷ 2 = 464,054.5

If the quotient is a whole number, then 2 and 464,054.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

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

1 928,109
-1 -928,109

Now, we try dividing 928,109 by 3:

928,109 ÷ 3 = 309,369.6667

If the quotient is a whole number, then 3 and 309,369.6667 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

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

1 928,109
-1 -928,109

Let's try dividing by 4:

928,109 ÷ 4 = 232,027.25

If the quotient is a whole number, then 4 and 232,027.25 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

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

1 928,109
-1 928,109
Keep dividing by the next highest number until you cannot divide anymore.

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

1713314749912173294036116371,4571,5192,3032,8214,27710,19918,94119,74729,93971,393132,587928,109
-1-7-13-31-47-49-91-217-329-403-611-637-1,457-1,519-2,303-2,821-4,277-10,199-18,941-19,747-29,939-71,393-132,587-928,109

More Examples

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