Q: What are the factor combinations of the number 125,122,249?

 A:
Positive:   1 x 1251222497 x 17874607157 x 796957257 x 486857443 x 2824431099 x 1138511799 x 695513101 x 40349
Negative: -1 x -125122249-7 x -17874607-157 x -796957-257 x -486857-443 x -282443-1099 x -113851-1799 x -69551-3101 x -40349


How do I find the factor combinations of the number 125,122,249?

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 125,122,249, 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.

1 125,122,249
-1 -125,122,249

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 125,122,249.

Example:
1 x 125,122,249 = 125,122,249
and
-1 x -125,122,249 = 125,122,249
Notice both answers equal 125,122,249

With that explanation out of the way, let's continue. Next, we take the number 125,122,249 and divide it by 2:

125,122,249 ÷ 2 = 62,561,124.5

If the quotient is a whole number, then 2 and 62,561,124.5 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:

1 125,122,249
-1 -125,122,249

Now, we try dividing 125,122,249 by 3:

125,122,249 ÷ 3 = 41,707,416.3333

If the quotient is a whole number, then 3 and 41,707,416.3333 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:

1 125,122,249
-1 -125,122,249

Let's try dividing by 4:

125,122,249 ÷ 4 = 31,280,562.25

If the quotient is a whole number, then 4 and 31,280,562.25 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:

1 125,122,249
-1 125,122,249
Keep dividing by the next highest number until you cannot divide anymore.

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

171572574431,0991,7993,10140,34969,551113,851282,443486,857796,95717,874,607125,122,249
-1-7-157-257-443-1,099-1,799-3,101-40,349-69,551-113,851-282,443-486,857-796,957-17,874,607-125,122,249

More Examples

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