Q: What are the factor combinations of the number 90,877,213?

 A:
Positive:   1 x 908772137 x 1298245929 x 313369731 x 293152349 x 1854637203 x 447671217 x 418789899 x 1010871421 x 639531519 x 598272063 x 440516293 x 14441
Negative: -1 x -90877213-7 x -12982459-29 x -3133697-31 x -2931523-49 x -1854637-203 x -447671-217 x -418789-899 x -101087-1421 x -63953-1519 x -59827-2063 x -44051-6293 x -14441


How do I find the factor combinations of the number 90,877,213?

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 90,877,213, 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 90,877,213
-1 -90,877,213

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 90,877,213.

Example:
1 x 90,877,213 = 90,877,213
and
-1 x -90,877,213 = 90,877,213
Notice both answers equal 90,877,213

With that explanation out of the way, let's continue. Next, we take the number 90,877,213 and divide it by 2:

90,877,213 ÷ 2 = 45,438,606.5

If the quotient is a whole number, then 2 and 45,438,606.5 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 90,877,213
-1 -90,877,213

Now, we try dividing 90,877,213 by 3:

90,877,213 ÷ 3 = 30,292,404.3333

If the quotient is a whole number, then 3 and 30,292,404.3333 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 90,877,213
-1 -90,877,213

Let's try dividing by 4:

90,877,213 ÷ 4 = 22,719,303.25

If the quotient is a whole number, then 4 and 22,719,303.25 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 90,877,213
-1 90,877,213
Keep dividing by the next highest number until you cannot divide anymore.

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

172931492032178991,4211,5192,0636,29314,44144,05159,82763,953101,087418,789447,6711,854,6372,931,5233,133,69712,982,45990,877,213
-1-7-29-31-49-203-217-899-1,421-1,519-2,063-6,293-14,441-44,051-59,827-63,953-101,087-418,789-447,671-1,854,637-2,931,523-3,133,697-12,982,459-90,877,213

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