Q: What are the factor combinations of the number 38,123,345?

 A:
Positive:   1 x 381233455 x 762466913 x 293256547 x 81113565 x 586513235 x 162227611 x 623953055 x 12479
Negative: -1 x -38123345-5 x -7624669-13 x -2932565-47 x -811135-65 x -586513-235 x -162227-611 x -62395-3055 x -12479


How do I find the factor combinations of the number 38,123,345?

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 38,123,345, 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 38,123,345
-1 -38,123,345

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 38,123,345.

Example:
1 x 38,123,345 = 38,123,345
and
-1 x -38,123,345 = 38,123,345
Notice both answers equal 38,123,345

With that explanation out of the way, let's continue. Next, we take the number 38,123,345 and divide it by 2:

38,123,345 ÷ 2 = 19,061,672.5

If the quotient is a whole number, then 2 and 19,061,672.5 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 38,123,345
-1 -38,123,345

Now, we try dividing 38,123,345 by 3:

38,123,345 ÷ 3 = 12,707,781.6667

If the quotient is a whole number, then 3 and 12,707,781.6667 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 38,123,345
-1 -38,123,345

Let's try dividing by 4:

38,123,345 ÷ 4 = 9,530,836.25

If the quotient is a whole number, then 4 and 9,530,836.25 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 38,123,345
-1 38,123,345
Keep dividing by the next highest number until you cannot divide anymore.

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

151347652356113,05512,47962,395162,227586,513811,1352,932,5657,624,66938,123,345
-1-5-13-47-65-235-611-3,055-12,479-62,395-162,227-586,513-811,135-2,932,565-7,624,669-38,123,345

More Examples

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