Q: What are the factor combinations of the number 5,601,421?

 A:
Positive:   1 x 56014217 x 80020331 x 18069183 x 67487217 x 25813311 x 18011581 x 96412177 x 2573
Negative: -1 x -5601421-7 x -800203-31 x -180691-83 x -67487-217 x -25813-311 x -18011-581 x -9641-2177 x -2573


How do I find the factor combinations of the number 5,601,421?

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 5,601,421, 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 5,601,421
-1 -5,601,421

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 5,601,421.

Example:
1 x 5,601,421 = 5,601,421
and
-1 x -5,601,421 = 5,601,421
Notice both answers equal 5,601,421

With that explanation out of the way, let's continue. Next, we take the number 5,601,421 and divide it by 2:

5,601,421 ÷ 2 = 2,800,710.5

If the quotient is a whole number, then 2 and 2,800,710.5 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 5,601,421
-1 -5,601,421

Now, we try dividing 5,601,421 by 3:

5,601,421 ÷ 3 = 1,867,140.3333

If the quotient is a whole number, then 3 and 1,867,140.3333 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 5,601,421
-1 -5,601,421

Let's try dividing by 4:

5,601,421 ÷ 4 = 1,400,355.25

If the quotient is a whole number, then 4 and 1,400,355.25 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 5,601,421
-1 5,601,421
Keep dividing by the next highest number until you cannot divide anymore.

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

1731832173115812,1772,5739,64118,01125,81367,487180,691800,2035,601,421
-1-7-31-83-217-311-581-2,177-2,573-9,641-18,011-25,813-67,487-180,691-800,203-5,601,421

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