Q: What are the factor combinations of the number 100,588,873?

 A:
Positive:   1 x 1005888737 x 1436983911 x 914444377 x 1306349103 x 976591121 x 831313721 x 139513847 x 1187591133 x 887811153 x 872417931 x 126838071 x 12463
Negative: -1 x -100588873-7 x -14369839-11 x -9144443-77 x -1306349-103 x -976591-121 x -831313-721 x -139513-847 x -118759-1133 x -88781-1153 x -87241-7931 x -12683-8071 x -12463


How do I find the factor combinations of the number 100,588,873?

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 100,588,873, 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.

1 100,588,873
-1 -100,588,873

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 100,588,873.

Example:
1 x 100,588,873 = 100,588,873
and
-1 x -100,588,873 = 100,588,873
Notice both answers equal 100,588,873

With that explanation out of the way, let's continue. Next, we take the number 100,588,873 and divide it by 2:

100,588,873 ÷ 2 = 50,294,436.5

If the quotient is a whole number, then 2 and 50,294,436.5 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:

1 100,588,873
-1 -100,588,873

Now, we try dividing 100,588,873 by 3:

100,588,873 ÷ 3 = 33,529,624.3333

If the quotient is a whole number, then 3 and 33,529,624.3333 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:

1 100,588,873
-1 -100,588,873

Let's try dividing by 4:

100,588,873 ÷ 4 = 25,147,218.25

If the quotient is a whole number, then 4 and 25,147,218.25 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:

1 100,588,873
-1 100,588,873
Keep dividing by the next highest number until you cannot divide anymore.

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

1711771031217218471,1331,1537,9318,07112,46312,68387,24188,781118,759139,513831,313976,5911,306,3499,144,44314,369,839100,588,873
-1-7-11-77-103-121-721-847-1,133-1,153-7,931-8,071-12,463-12,683-87,241-88,781-118,759-139,513-831,313-976,591-1,306,349-9,144,443-14,369,839-100,588,873

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