Q: What are the factor combinations of the number 87,002,305?

 A:
Positive:   1 x 870023055 x 1740046113 x 669248565 x 133849779 x 1101295395 x 2202591027 x 847155135 x 16943
Negative: -1 x -87002305-5 x -17400461-13 x -6692485-65 x -1338497-79 x -1101295-395 x -220259-1027 x -84715-5135 x -16943


How do I find the factor combinations of the number 87,002,305?

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 87,002,305, 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 87,002,305
-1 -87,002,305

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 87,002,305.

Example:
1 x 87,002,305 = 87,002,305
and
-1 x -87,002,305 = 87,002,305
Notice both answers equal 87,002,305

With that explanation out of the way, let's continue. Next, we take the number 87,002,305 and divide it by 2:

87,002,305 ÷ 2 = 43,501,152.5

If the quotient is a whole number, then 2 and 43,501,152.5 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 87,002,305
-1 -87,002,305

Now, we try dividing 87,002,305 by 3:

87,002,305 ÷ 3 = 29,000,768.3333

If the quotient is a whole number, then 3 and 29,000,768.3333 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 87,002,305
-1 -87,002,305

Let's try dividing by 4:

87,002,305 ÷ 4 = 21,750,576.25

If the quotient is a whole number, then 4 and 21,750,576.25 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 87,002,305
-1 87,002,305
Keep dividing by the next highest number until you cannot divide anymore.

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

151365793951,0275,13516,94384,715220,2591,101,2951,338,4976,692,48517,400,46187,002,305
-1-5-13-65-79-395-1,027-5,135-16,943-84,715-220,259-1,101,295-1,338,497-6,692,485-17,400,461-87,002,305

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