Q: What are the factor combinations of the number 125,502,421?

 A:
Positive:   1 x 12550242111 x 1140931123 x 5456627233 x 538637253 x 4960572129 x 589492563 x 489675359 x 23419
Negative: -1 x -125502421-11 x -11409311-23 x -5456627-233 x -538637-253 x -496057-2129 x -58949-2563 x -48967-5359 x -23419


How do I find the factor combinations of the number 125,502,421?

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 125,502,421, 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.

1 125,502,421
-1 -125,502,421

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 125,502,421.

Example:
1 x 125,502,421 = 125,502,421
and
-1 x -125,502,421 = 125,502,421
Notice both answers equal 125,502,421

With that explanation out of the way, let's continue. Next, we take the number 125,502,421 and divide it by 2:

125,502,421 ÷ 2 = 62,751,210.5

If the quotient is a whole number, then 2 and 62,751,210.5 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:

1 125,502,421
-1 -125,502,421

Now, we try dividing 125,502,421 by 3:

125,502,421 ÷ 3 = 41,834,140.3333

If the quotient is a whole number, then 3 and 41,834,140.3333 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:

1 125,502,421
-1 -125,502,421

Let's try dividing by 4:

125,502,421 ÷ 4 = 31,375,605.25

If the quotient is a whole number, then 4 and 31,375,605.25 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:

1 125,502,421
-1 125,502,421
Keep dividing by the next highest number until you cannot divide anymore.

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

111232332532,1292,5635,35923,41948,96758,949496,057538,6375,456,62711,409,311125,502,421
-1-11-23-233-253-2,129-2,563-5,359-23,419-48,967-58,949-496,057-538,637-5,456,627-11,409,311-125,502,421

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