Q: What are the factor combinations of the number 10,502,525?

 A:
Positive:   1 x 105025255 x 210050511 x 95477525 x 42010155 x 190955181 x 58025211 x 49775275 x 38191905 x 116051055 x 99551991 x 52752321 x 4525
Negative: -1 x -10502525-5 x -2100505-11 x -954775-25 x -420101-55 x -190955-181 x -58025-211 x -49775-275 x -38191-905 x -11605-1055 x -9955-1991 x -5275-2321 x -4525


How do I find the factor combinations of the number 10,502,525?

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 10,502,525, 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 10,502,525
-1 -10,502,525

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 10,502,525.

Example:
1 x 10,502,525 = 10,502,525
and
-1 x -10,502,525 = 10,502,525
Notice both answers equal 10,502,525

With that explanation out of the way, let's continue. Next, we take the number 10,502,525 and divide it by 2:

10,502,525 ÷ 2 = 5,251,262.5

If the quotient is a whole number, then 2 and 5,251,262.5 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 10,502,525
-1 -10,502,525

Now, we try dividing 10,502,525 by 3:

10,502,525 ÷ 3 = 3,500,841.6667

If the quotient is a whole number, then 3 and 3,500,841.6667 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 10,502,525
-1 -10,502,525

Let's try dividing by 4:

10,502,525 ÷ 4 = 2,625,631.25

If the quotient is a whole number, then 4 and 2,625,631.25 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 10,502,525
-1 10,502,525
Keep dividing by the next highest number until you cannot divide anymore.

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

151125551812112759051,0551,9912,3214,5255,2759,95511,60538,19149,77558,025190,955420,101954,7752,100,50510,502,525
-1-5-11-25-55-181-211-275-905-1,055-1,991-2,321-4,525-5,275-9,955-11,605-38,191-49,775-58,025-190,955-420,101-954,775-2,100,505-10,502,525

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