Q: What are the factor combinations of the number 25,010,105?

 A:
Positive:   1 x 250101055 x 500202171 x 352255355 x 70451
Negative: -1 x -25010105-5 x -5002021-71 x -352255-355 x -70451


How do I find the factor combinations of the number 25,010,105?

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 25,010,105, 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 25,010,105
-1 -25,010,105

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 25,010,105.

Example:
1 x 25,010,105 = 25,010,105
and
-1 x -25,010,105 = 25,010,105
Notice both answers equal 25,010,105

With that explanation out of the way, let's continue. Next, we take the number 25,010,105 and divide it by 2:

25,010,105 ÷ 2 = 12,505,052.5

If the quotient is a whole number, then 2 and 12,505,052.5 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 25,010,105
-1 -25,010,105

Now, we try dividing 25,010,105 by 3:

25,010,105 ÷ 3 = 8,336,701.6667

If the quotient is a whole number, then 3 and 8,336,701.6667 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 25,010,105
-1 -25,010,105

Let's try dividing by 4:

25,010,105 ÷ 4 = 6,252,526.25

If the quotient is a whole number, then 4 and 6,252,526.25 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 25,010,105
-1 25,010,105
Keep dividing by the next highest number until you cannot divide anymore.

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

157135570,451352,2555,002,02125,010,105
-1-5-71-355-70,451-352,255-5,002,021-25,010,105

More Examples

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