Q: What are the factor combinations of the number 42,213,413?

 A:
Positive:   1 x 4221341311 x 383758331 x 136172379 x 534347341 x 123793869 x 485771567 x 269392449 x 17237
Negative: -1 x -42213413-11 x -3837583-31 x -1361723-79 x -534347-341 x -123793-869 x -48577-1567 x -26939-2449 x -17237


How do I find the factor combinations of the number 42,213,413?

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 42,213,413, 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 42,213,413
-1 -42,213,413

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 42,213,413.

Example:
1 x 42,213,413 = 42,213,413
and
-1 x -42,213,413 = 42,213,413
Notice both answers equal 42,213,413

With that explanation out of the way, let's continue. Next, we take the number 42,213,413 and divide it by 2:

42,213,413 ÷ 2 = 21,106,706.5

If the quotient is a whole number, then 2 and 21,106,706.5 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 42,213,413
-1 -42,213,413

Now, we try dividing 42,213,413 by 3:

42,213,413 ÷ 3 = 14,071,137.6667

If the quotient is a whole number, then 3 and 14,071,137.6667 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 42,213,413
-1 -42,213,413

Let's try dividing by 4:

42,213,413 ÷ 4 = 10,553,353.25

If the quotient is a whole number, then 4 and 10,553,353.25 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 42,213,413
-1 42,213,413
Keep dividing by the next highest number until you cannot divide anymore.

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

11131793418691,5672,44917,23726,93948,577123,793534,3471,361,7233,837,58342,213,413
-1-11-31-79-341-869-1,567-2,449-17,237-26,939-48,577-123,793-534,347-1,361,723-3,837,583-42,213,413

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