Q: What are the factor combinations of the number 42,220,109?

 A:
Positive:   1 x 4222010919 x 222211131 x 136193943 x 981863589 x 71681817 x 516771333 x 316731667 x 25327
Negative: -1 x -42220109-19 x -2222111-31 x -1361939-43 x -981863-589 x -71681-817 x -51677-1333 x -31673-1667 x -25327


How do I find the factor combinations of the number 42,220,109?

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 42,220,109, 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 42,220,109
-1 -42,220,109

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 42,220,109.

Example:
1 x 42,220,109 = 42,220,109
and
-1 x -42,220,109 = 42,220,109
Notice both answers equal 42,220,109

With that explanation out of the way, let's continue. Next, we take the number 42,220,109 and divide it by 2:

42,220,109 ÷ 2 = 21,110,054.5

If the quotient is a whole number, then 2 and 21,110,054.5 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 42,220,109
-1 -42,220,109

Now, we try dividing 42,220,109 by 3:

42,220,109 ÷ 3 = 14,073,369.6667

If the quotient is a whole number, then 3 and 14,073,369.6667 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 42,220,109
-1 -42,220,109

Let's try dividing by 4:

42,220,109 ÷ 4 = 10,555,027.25

If the quotient is a whole number, then 4 and 10,555,027.25 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 42,220,109
-1 42,220,109
Keep dividing by the next highest number until you cannot divide anymore.

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

11931435898171,3331,66725,32731,67351,67771,681981,8631,361,9392,222,11142,220,109
-1-19-31-43-589-817-1,333-1,667-25,327-31,673-51,677-71,681-981,863-1,361,939-2,222,111-42,220,109

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