Q: What are the factor combinations of the number 84,090,523?

 A:
Positive:   1 x 8409052311 x 764459319 x 442581779 x 1064437121 x 694963209 x 402347463 x 181621869 x 967671501 x 560232299 x 365775093 x 165118797 x 9559
Negative: -1 x -84090523-11 x -7644593-19 x -4425817-79 x -1064437-121 x -694963-209 x -402347-463 x -181621-869 x -96767-1501 x -56023-2299 x -36577-5093 x -16511-8797 x -9559


How do I find the factor combinations of the number 84,090,523?

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 84,090,523, 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 84,090,523
-1 -84,090,523

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 84,090,523.

Example:
1 x 84,090,523 = 84,090,523
and
-1 x -84,090,523 = 84,090,523
Notice both answers equal 84,090,523

With that explanation out of the way, let's continue. Next, we take the number 84,090,523 and divide it by 2:

84,090,523 ÷ 2 = 42,045,261.5

If the quotient is a whole number, then 2 and 42,045,261.5 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 84,090,523
-1 -84,090,523

Now, we try dividing 84,090,523 by 3:

84,090,523 ÷ 3 = 28,030,174.3333

If the quotient is a whole number, then 3 and 28,030,174.3333 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 84,090,523
-1 -84,090,523

Let's try dividing by 4:

84,090,523 ÷ 4 = 21,022,630.75

If the quotient is a whole number, then 4 and 21,022,630.75 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 84,090,523
-1 84,090,523
Keep dividing by the next highest number until you cannot divide anymore.

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

11119791212094638691,5012,2995,0938,7979,55916,51136,57756,02396,767181,621402,347694,9631,064,4374,425,8177,644,59384,090,523
-1-11-19-79-121-209-463-869-1,501-2,299-5,093-8,797-9,559-16,511-36,577-56,023-96,767-181,621-402,347-694,963-1,064,437-4,425,817-7,644,593-84,090,523

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