Q: What are the factor combinations of the number 1,680,025?

 A:
Positive:   1 x 16800255 x 33600517 x 9882525 x 6720159 x 2847567 x 2507585 x 19765295 x 5695335 x 5015425 x 39531003 x 16751139 x 1475
Negative: -1 x -1680025-5 x -336005-17 x -98825-25 x -67201-59 x -28475-67 x -25075-85 x -19765-295 x -5695-335 x -5015-425 x -3953-1003 x -1675-1139 x -1475


How do I find the factor combinations of the number 1,680,025?

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 1,680,025, 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 1,680,025
-1 -1,680,025

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 1,680,025.

Example:
1 x 1,680,025 = 1,680,025
and
-1 x -1,680,025 = 1,680,025
Notice both answers equal 1,680,025

With that explanation out of the way, let's continue. Next, we take the number 1,680,025 and divide it by 2:

1,680,025 ÷ 2 = 840,012.5

If the quotient is a whole number, then 2 and 840,012.5 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 1,680,025
-1 -1,680,025

Now, we try dividing 1,680,025 by 3:

1,680,025 ÷ 3 = 560,008.3333

If the quotient is a whole number, then 3 and 560,008.3333 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 1,680,025
-1 -1,680,025

Let's try dividing by 4:

1,680,025 ÷ 4 = 420,006.25

If the quotient is a whole number, then 4 and 420,006.25 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 1,680,025
-1 1,680,025
Keep dividing by the next highest number until you cannot divide anymore.

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

1517255967852953354251,0031,1391,4751,6753,9535,0155,69519,76525,07528,47567,20198,825336,0051,680,025
-1-5-17-25-59-67-85-295-335-425-1,003-1,139-1,475-1,675-3,953-5,015-5,695-19,765-25,075-28,475-67,201-98,825-336,005-1,680,025

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