Q: What are the factor combinations of the number 2,500,105?

 A:
Positive:   1 x 25001055 x 50002117 x 14706567 x 3731585 x 29413335 x 7463439 x 56951139 x 2195
Negative: -1 x -2500105-5 x -500021-17 x -147065-67 x -37315-85 x -29413-335 x -7463-439 x -5695-1139 x -2195


How do I find the factor combinations of the number 2,500,105?

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 2,500,105, 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 2,500,105
-1 -2,500,105

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 2,500,105.

Example:
1 x 2,500,105 = 2,500,105
and
-1 x -2,500,105 = 2,500,105
Notice both answers equal 2,500,105

With that explanation out of the way, let's continue. Next, we take the number 2,500,105 and divide it by 2:

2,500,105 ÷ 2 = 1,250,052.5

If the quotient is a whole number, then 2 and 1,250,052.5 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 2,500,105
-1 -2,500,105

Now, we try dividing 2,500,105 by 3:

2,500,105 ÷ 3 = 833,368.3333

If the quotient is a whole number, then 3 and 833,368.3333 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 2,500,105
-1 -2,500,105

Let's try dividing by 4:

2,500,105 ÷ 4 = 625,026.25

If the quotient is a whole number, then 4 and 625,026.25 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 2,500,105
-1 2,500,105
Keep dividing by the next highest number until you cannot divide anymore.

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

151767853354391,1392,1955,6957,46329,41337,315147,065500,0212,500,105
-1-5-17-67-85-335-439-1,139-2,195-5,695-7,463-29,413-37,315-147,065-500,021-2,500,105

More Examples

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