Q: What are the factor combinations of the number 413,424,403?

 A:
Positive:   1 x 4134244037 x 5906062943 x 9614521301 x 13735031163 x 3554811181 x 3500638141 x 507838267 x 50009
Negative: -1 x -413424403-7 x -59060629-43 x -9614521-301 x -1373503-1163 x -355481-1181 x -350063-8141 x -50783-8267 x -50009


How do I find the factor combinations of the number 413,424,403?

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 413,424,403, 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.

1 413,424,403
-1 -413,424,403

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 413,424,403.

Example:
1 x 413,424,403 = 413,424,403
and
-1 x -413,424,403 = 413,424,403
Notice both answers equal 413,424,403

With that explanation out of the way, let's continue. Next, we take the number 413,424,403 and divide it by 2:

413,424,403 ÷ 2 = 206,712,201.5

If the quotient is a whole number, then 2 and 206,712,201.5 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:

1 413,424,403
-1 -413,424,403

Now, we try dividing 413,424,403 by 3:

413,424,403 ÷ 3 = 137,808,134.3333

If the quotient is a whole number, then 3 and 137,808,134.3333 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:

1 413,424,403
-1 -413,424,403

Let's try dividing by 4:

413,424,403 ÷ 4 = 103,356,100.75

If the quotient is a whole number, then 4 and 103,356,100.75 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:

1 413,424,403
-1 413,424,403
Keep dividing by the next highest number until you cannot divide anymore.

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

17433011,1631,1818,1418,26750,00950,783350,063355,4811,373,5039,614,52159,060,629413,424,403
-1-7-43-301-1,163-1,181-8,141-8,267-50,009-50,783-350,063-355,481-1,373,503-9,614,521-59,060,629-413,424,403

More Examples

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