Q: What are the factor combinations of the number 12,501,035?

 A:
Positive:   1 x 125010355 x 250020717 x 73535561 x 20493585 x 147071305 x 409871037 x 120552411 x 5185
Negative: -1 x -12501035-5 x -2500207-17 x -735355-61 x -204935-85 x -147071-305 x -40987-1037 x -12055-2411 x -5185


How do I find the factor combinations of the number 12,501,035?

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 12,501,035, 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 12,501,035
-1 -12,501,035

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 12,501,035.

Example:
1 x 12,501,035 = 12,501,035
and
-1 x -12,501,035 = 12,501,035
Notice both answers equal 12,501,035

With that explanation out of the way, let's continue. Next, we take the number 12,501,035 and divide it by 2:

12,501,035 ÷ 2 = 6,250,517.5

If the quotient is a whole number, then 2 and 6,250,517.5 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 12,501,035
-1 -12,501,035

Now, we try dividing 12,501,035 by 3:

12,501,035 ÷ 3 = 4,167,011.6667

If the quotient is a whole number, then 3 and 4,167,011.6667 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 12,501,035
-1 -12,501,035

Let's try dividing by 4:

12,501,035 ÷ 4 = 3,125,258.75

If the quotient is a whole number, then 4 and 3,125,258.75 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 12,501,035
-1 12,501,035
Keep dividing by the next highest number until you cannot divide anymore.

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

151761853051,0372,4115,18512,05540,987147,071204,935735,3552,500,20712,501,035
-1-5-17-61-85-305-1,037-2,411-5,185-12,055-40,987-147,071-204,935-735,355-2,500,207-12,501,035

More Examples

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