Q: What are the factor combinations of the number 41,124,013?

 A:
Positive:   1 x 411240137 x 587485947 x 874979239 x 172067329 x 124997523 x 786311673 x 245813661 x 11233
Negative: -1 x -41124013-7 x -5874859-47 x -874979-239 x -172067-329 x -124997-523 x -78631-1673 x -24581-3661 x -11233


How do I find the factor combinations of the number 41,124,013?

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 41,124,013, 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 41,124,013
-1 -41,124,013

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 41,124,013.

Example:
1 x 41,124,013 = 41,124,013
and
-1 x -41,124,013 = 41,124,013
Notice both answers equal 41,124,013

With that explanation out of the way, let's continue. Next, we take the number 41,124,013 and divide it by 2:

41,124,013 ÷ 2 = 20,562,006.5

If the quotient is a whole number, then 2 and 20,562,006.5 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 41,124,013
-1 -41,124,013

Now, we try dividing 41,124,013 by 3:

41,124,013 ÷ 3 = 13,708,004.3333

If the quotient is a whole number, then 3 and 13,708,004.3333 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 41,124,013
-1 -41,124,013

Let's try dividing by 4:

41,124,013 ÷ 4 = 10,281,003.25

If the quotient is a whole number, then 4 and 10,281,003.25 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 41,124,013
-1 41,124,013
Keep dividing by the next highest number until you cannot divide anymore.

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

17472393295231,6733,66111,23324,58178,631124,997172,067874,9795,874,85941,124,013
-1-7-47-239-329-523-1,673-3,661-11,233-24,581-78,631-124,997-172,067-874,979-5,874,859-41,124,013

More Examples

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