Q: What are the factor combinations of the number 404,424,041?

 A:
Positive:   1 x 4044240417 x 5777486341 x 9864001103 x 3926447287 x 1409143721 x 5609214223 x 9576713681 x 29561
Negative: -1 x -404424041-7 x -57774863-41 x -9864001-103 x -3926447-287 x -1409143-721 x -560921-4223 x -95767-13681 x -29561


How do I find the factor combinations of the number 404,424,041?

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 404,424,041, 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.

1 404,424,041
-1 -404,424,041

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 404,424,041.

Example:
1 x 404,424,041 = 404,424,041
and
-1 x -404,424,041 = 404,424,041
Notice both answers equal 404,424,041

With that explanation out of the way, let's continue. Next, we take the number 404,424,041 and divide it by 2:

404,424,041 ÷ 2 = 202,212,020.5

If the quotient is a whole number, then 2 and 202,212,020.5 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:

1 404,424,041
-1 -404,424,041

Now, we try dividing 404,424,041 by 3:

404,424,041 ÷ 3 = 134,808,013.6667

If the quotient is a whole number, then 3 and 134,808,013.6667 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:

1 404,424,041
-1 -404,424,041

Let's try dividing by 4:

404,424,041 ÷ 4 = 101,106,010.25

If the quotient is a whole number, then 4 and 101,106,010.25 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:

1 404,424,041
-1 404,424,041
Keep dividing by the next highest number until you cannot divide anymore.

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

17411032877214,22313,68129,56195,767560,9211,409,1433,926,4479,864,00157,774,863404,424,041
-1-7-41-103-287-721-4,223-13,681-29,561-95,767-560,921-1,409,143-3,926,447-9,864,001-57,774,863-404,424,041

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