Q: What are the factor combinations of the number 686,684,377?

 A:
Positive:   1 x 68668437719 x 3614128353 x 12956309107 x 64176111007 x 6819112033 x 3377695671 x 1210876373 x 107749
Negative: -1 x -686684377-19 x -36141283-53 x -12956309-107 x -6417611-1007 x -681911-2033 x -337769-5671 x -121087-6373 x -107749


How do I find the factor combinations of the number 686,684,377?

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 686,684,377, 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.

1 686,684,377
-1 -686,684,377

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 686,684,377.

Example:
1 x 686,684,377 = 686,684,377
and
-1 x -686,684,377 = 686,684,377
Notice both answers equal 686,684,377

With that explanation out of the way, let's continue. Next, we take the number 686,684,377 and divide it by 2:

686,684,377 ÷ 2 = 343,342,188.5

If the quotient is a whole number, then 2 and 343,342,188.5 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:

1 686,684,377
-1 -686,684,377

Now, we try dividing 686,684,377 by 3:

686,684,377 ÷ 3 = 228,894,792.3333

If the quotient is a whole number, then 3 and 228,894,792.3333 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:

1 686,684,377
-1 -686,684,377

Let's try dividing by 4:

686,684,377 ÷ 4 = 171,671,094.25

If the quotient is a whole number, then 4 and 171,671,094.25 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:

1 686,684,377
-1 686,684,377
Keep dividing by the next highest number until you cannot divide anymore.

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

119531071,0072,0335,6716,373107,749121,087337,769681,9116,417,61112,956,30936,141,283686,684,377
-1-19-53-107-1,007-2,033-5,671-6,373-107,749-121,087-337,769-681,911-6,417,611-12,956,309-36,141,283-686,684,377

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