Q: What are the factor combinations of the number 125,408,657?

 A:
Positive:   1 x 12540865711 x 1140078767 x 1871771263 x 476839647 x 193831737 x 1701612893 x 433497117 x 17621
Negative: -1 x -125408657-11 x -11400787-67 x -1871771-263 x -476839-647 x -193831-737 x -170161-2893 x -43349-7117 x -17621


How do I find the factor combinations of the number 125,408,657?

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 125,408,657, 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.

1 125,408,657
-1 -125,408,657

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 125,408,657.

Example:
1 x 125,408,657 = 125,408,657
and
-1 x -125,408,657 = 125,408,657
Notice both answers equal 125,408,657

With that explanation out of the way, let's continue. Next, we take the number 125,408,657 and divide it by 2:

125,408,657 ÷ 2 = 62,704,328.5

If the quotient is a whole number, then 2 and 62,704,328.5 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:

1 125,408,657
-1 -125,408,657

Now, we try dividing 125,408,657 by 3:

125,408,657 ÷ 3 = 41,802,885.6667

If the quotient is a whole number, then 3 and 41,802,885.6667 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:

1 125,408,657
-1 -125,408,657

Let's try dividing by 4:

125,408,657 ÷ 4 = 31,352,164.25

If the quotient is a whole number, then 4 and 31,352,164.25 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:

1 125,408,657
-1 125,408,657
Keep dividing by the next highest number until you cannot divide anymore.

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

111672636477372,8937,11717,62143,349170,161193,831476,8391,871,77111,400,787125,408,657
-1-11-67-263-647-737-2,893-7,117-17,621-43,349-170,161-193,831-476,839-1,871,771-11,400,787-125,408,657

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