Q: What are the factor combinations of the number 1,688,525?

 A:
Positive:   1 x 16885255 x 33770517 x 9932525 x 6754129 x 5822585 x 19865137 x 12325145 x 11645425 x 3973493 x 3425685 x 2465725 x 2329
Negative: -1 x -1688525-5 x -337705-17 x -99325-25 x -67541-29 x -58225-85 x -19865-137 x -12325-145 x -11645-425 x -3973-493 x -3425-685 x -2465-725 x -2329


How do I find the factor combinations of the number 1,688,525?

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 1,688,525, 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 1,688,525
-1 -1,688,525

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 1,688,525.

Example:
1 x 1,688,525 = 1,688,525
and
-1 x -1,688,525 = 1,688,525
Notice both answers equal 1,688,525

With that explanation out of the way, let's continue. Next, we take the number 1,688,525 and divide it by 2:

1,688,525 ÷ 2 = 844,262.5

If the quotient is a whole number, then 2 and 844,262.5 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 1,688,525
-1 -1,688,525

Now, we try dividing 1,688,525 by 3:

1,688,525 ÷ 3 = 562,841.6667

If the quotient is a whole number, then 3 and 562,841.6667 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 1,688,525
-1 -1,688,525

Let's try dividing by 4:

1,688,525 ÷ 4 = 422,131.25

If the quotient is a whole number, then 4 and 422,131.25 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 1,688,525
-1 1,688,525
Keep dividing by the next highest number until you cannot divide anymore.

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

15172529851371454254936857252,3292,4653,4253,97311,64512,32519,86558,22567,54199,325337,7051,688,525
-1-5-17-25-29-85-137-145-425-493-685-725-2,329-2,465-3,425-3,973-11,645-12,325-19,865-58,225-67,541-99,325-337,705-1,688,525

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