Q: What are the factor combinations of the number 686,452,188?

 A:
Positive:   1 x 6864521882 x 3432260943 x 2288173964 x 1716130476 x 11440869812 x 57204349
Negative: -1 x -686452188-2 x -343226094-3 x -228817396-4 x -171613047-6 x -114408698-12 x -57204349


How do I find the factor combinations of the number 686,452,188?

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 686,452,188, 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.

1 686,452,188
-1 -686,452,188

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 686,452,188.

Example:
1 x 686,452,188 = 686,452,188
and
-1 x -686,452,188 = 686,452,188
Notice both answers equal 686,452,188

With that explanation out of the way, let's continue. Next, we take the number 686,452,188 and divide it by 2:

686,452,188 ÷ 2 = 343,226,094

If the quotient is a whole number, then 2 and 343,226,094 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 343,226,094 686,452,188
-1 -2 -343,226,094 -686,452,188

Now, we try dividing 686,452,188 by 3:

686,452,188 ÷ 3 = 228,817,396

If the quotient is a whole number, then 3 and 228,817,396 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 228,817,396 343,226,094 686,452,188
-1 -2 -3 -228,817,396 -343,226,094 -686,452,188

Let's try dividing by 4:

686,452,188 ÷ 4 = 171,613,047

If the quotient is a whole number, then 4 and 171,613,047 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 171,613,047 228,817,396 343,226,094 686,452,188
-1 -2 -3 -4 -171,613,047 -228,817,396 -343,226,094 686,452,188
Keep dividing by the next highest number until you cannot divide anymore.

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

123461257,204,349114,408,698171,613,047228,817,396343,226,094686,452,188
-1-2-3-4-6-12-57,204,349-114,408,698-171,613,047-228,817,396-343,226,094-686,452,188

More Examples

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