Q: What are the factor combinations of the number 686,375?

 A:
Positive:   1 x 6863755 x 13727517 x 4037519 x 3612525 x 2745585 x 807595 x 7225125 x 5491289 x 2375323 x 2125425 x 1615475 x 1445
Negative: -1 x -686375-5 x -137275-17 x -40375-19 x -36125-25 x -27455-85 x -8075-95 x -7225-125 x -5491-289 x -2375-323 x -2125-425 x -1615-475 x -1445


How do I find the factor combinations of the number 686,375?

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 686,375, 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.

1 686,375
-1 -686,375

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 686,375.

Example:
1 x 686,375 = 686,375
and
-1 x -686,375 = 686,375
Notice both answers equal 686,375

With that explanation out of the way, let's continue. Next, we take the number 686,375 and divide it by 2:

686,375 ÷ 2 = 343,187.5

If the quotient is a whole number, then 2 and 343,187.5 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:

1 686,375
-1 -686,375

Now, we try dividing 686,375 by 3:

686,375 ÷ 3 = 228,791.6667

If the quotient is a whole number, then 3 and 228,791.6667 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:

1 686,375
-1 -686,375

Let's try dividing by 4:

686,375 ÷ 4 = 171,593.75

If the quotient is a whole number, then 4 and 171,593.75 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:

1 686,375
-1 686,375
Keep dividing by the next highest number until you cannot divide anymore.

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

1517192585951252893234254751,4451,6152,1252,3755,4917,2258,07527,45536,12540,375137,275686,375
-1-5-17-19-25-85-95-125-289-323-425-475-1,445-1,615-2,125-2,375-5,491-7,225-8,075-27,455-36,125-40,375-137,275-686,375

More Examples

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