Q: What are the factor combinations of the number 103,022,125?

 A:
Positive:   1 x 1030221255 x 2060442517 x 606012525 x 412088585 x 1212025125 x 824177425 x 2424052125 x 48481
Negative: -1 x -103022125-5 x -20604425-17 x -6060125-25 x -4120885-85 x -1212025-125 x -824177-425 x -242405-2125 x -48481


How do I find the factor combinations of the number 103,022,125?

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 103,022,125, 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.

1 103,022,125
-1 -103,022,125

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 103,022,125.

Example:
1 x 103,022,125 = 103,022,125
and
-1 x -103,022,125 = 103,022,125
Notice both answers equal 103,022,125

With that explanation out of the way, let's continue. Next, we take the number 103,022,125 and divide it by 2:

103,022,125 ÷ 2 = 51,511,062.5

If the quotient is a whole number, then 2 and 51,511,062.5 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:

1 103,022,125
-1 -103,022,125

Now, we try dividing 103,022,125 by 3:

103,022,125 ÷ 3 = 34,340,708.3333

If the quotient is a whole number, then 3 and 34,340,708.3333 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:

1 103,022,125
-1 -103,022,125

Let's try dividing by 4:

103,022,125 ÷ 4 = 25,755,531.25

If the quotient is a whole number, then 4 and 25,755,531.25 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:

1 103,022,125
-1 103,022,125
Keep dividing by the next highest number until you cannot divide anymore.

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

151725851254252,12548,481242,405824,1771,212,0254,120,8856,060,12520,604,425103,022,125
-1-5-17-25-85-125-425-2,125-48,481-242,405-824,177-1,212,025-4,120,885-6,060,125-20,604,425-103,022,125

More Examples

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