Q: What are the factor combinations of the number 8,506,421?

 A:
Positive:   1 x 85064217 x 121520311 x 77331177 x 11047383 x 102487121 x 70301581 x 14641847 x 10043913 x 93171331 x 6391
Negative: -1 x -8506421-7 x -1215203-11 x -773311-77 x -110473-83 x -102487-121 x -70301-581 x -14641-847 x -10043-913 x -9317-1331 x -6391


How do I find the factor combinations of the number 8,506,421?

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 8,506,421, 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 8,506,421
-1 -8,506,421

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 8,506,421.

Example:
1 x 8,506,421 = 8,506,421
and
-1 x -8,506,421 = 8,506,421
Notice both answers equal 8,506,421

With that explanation out of the way, let's continue. Next, we take the number 8,506,421 and divide it by 2:

8,506,421 ÷ 2 = 4,253,210.5

If the quotient is a whole number, then 2 and 4,253,210.5 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 8,506,421
-1 -8,506,421

Now, we try dividing 8,506,421 by 3:

8,506,421 ÷ 3 = 2,835,473.6667

If the quotient is a whole number, then 3 and 2,835,473.6667 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 8,506,421
-1 -8,506,421

Let's try dividing by 4:

8,506,421 ÷ 4 = 2,126,605.25

If the quotient is a whole number, then 4 and 2,126,605.25 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 8,506,421
-1 8,506,421
Keep dividing by the next highest number until you cannot divide anymore.

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

171177831215818479131,3316,3919,31710,04314,64170,301102,487110,473773,3111,215,2038,506,421
-1-7-11-77-83-121-581-847-913-1,331-6,391-9,317-10,043-14,641-70,301-102,487-110,473-773,311-1,215,203-8,506,421

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