Q: What are the factor combinations of the number 688,685,705?

 A:
Positive:   1 x 6886857055 x 137737141107 x 6436315383 x 1798135535 x 12872631915 x 3596273361 x 20490516805 x 40981
Negative: -1 x -688685705-5 x -137737141-107 x -6436315-383 x -1798135-535 x -1287263-1915 x -359627-3361 x -204905-16805 x -40981


How do I find the factor combinations of the number 688,685,705?

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 688,685,705, 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.

1 688,685,705
-1 -688,685,705

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 688,685,705.

Example:
1 x 688,685,705 = 688,685,705
and
-1 x -688,685,705 = 688,685,705
Notice both answers equal 688,685,705

With that explanation out of the way, let's continue. Next, we take the number 688,685,705 and divide it by 2:

688,685,705 ÷ 2 = 344,342,852.5

If the quotient is a whole number, then 2 and 344,342,852.5 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:

1 688,685,705
-1 -688,685,705

Now, we try dividing 688,685,705 by 3:

688,685,705 ÷ 3 = 229,561,901.6667

If the quotient is a whole number, then 3 and 229,561,901.6667 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:

1 688,685,705
-1 -688,685,705

Let's try dividing by 4:

688,685,705 ÷ 4 = 172,171,426.25

If the quotient is a whole number, then 4 and 172,171,426.25 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:

1 688,685,705
-1 688,685,705
Keep dividing by the next highest number until you cannot divide anymore.

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

151073835351,9153,36116,80540,981204,905359,6271,287,2631,798,1356,436,315137,737,141688,685,705
-1-5-107-383-535-1,915-3,361-16,805-40,981-204,905-359,627-1,287,263-1,798,135-6,436,315-137,737,141-688,685,705

More Examples

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