Q: What are the factor combinations of the number 42,204,425?

 A:
Positive:   1 x 422044255 x 844088523 x 183497525 x 168817729 x 1455325115 x 366995145 x 291065575 x 73399667 x 63275725 x 582132531 x 166753335 x 12655
Negative: -1 x -42204425-5 x -8440885-23 x -1834975-25 x -1688177-29 x -1455325-115 x -366995-145 x -291065-575 x -73399-667 x -63275-725 x -58213-2531 x -16675-3335 x -12655


How do I find the factor combinations of the number 42,204,425?

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 42,204,425, 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 42,204,425
-1 -42,204,425

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 42,204,425.

Example:
1 x 42,204,425 = 42,204,425
and
-1 x -42,204,425 = 42,204,425
Notice both answers equal 42,204,425

With that explanation out of the way, let's continue. Next, we take the number 42,204,425 and divide it by 2:

42,204,425 ÷ 2 = 21,102,212.5

If the quotient is a whole number, then 2 and 21,102,212.5 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 42,204,425
-1 -42,204,425

Now, we try dividing 42,204,425 by 3:

42,204,425 ÷ 3 = 14,068,141.6667

If the quotient is a whole number, then 3 and 14,068,141.6667 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 42,204,425
-1 -42,204,425

Let's try dividing by 4:

42,204,425 ÷ 4 = 10,551,106.25

If the quotient is a whole number, then 4 and 10,551,106.25 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 42,204,425
-1 42,204,425
Keep dividing by the next highest number until you cannot divide anymore.

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

152325291151455756677252,5313,33512,65516,67558,21363,27573,399291,065366,9951,455,3251,688,1771,834,9758,440,88542,204,425
-1-5-23-25-29-115-145-575-667-725-2,531-3,335-12,655-16,675-58,213-63,275-73,399-291,065-366,995-1,455,325-1,688,177-1,834,975-8,440,885-42,204,425

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