Q: What are the factor combinations of the number 23,053,525?

 A:
Positive:   1 x 230535255 x 461070511 x 209577525 x 92214155 x 419155121 x 190525275 x 83831605 x 381053025 x 7621
Negative: -1 x -23053525-5 x -4610705-11 x -2095775-25 x -922141-55 x -419155-121 x -190525-275 x -83831-605 x -38105-3025 x -7621


How do I find the factor combinations of the number 23,053,525?

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 23,053,525, 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 23,053,525
-1 -23,053,525

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 23,053,525.

Example:
1 x 23,053,525 = 23,053,525
and
-1 x -23,053,525 = 23,053,525
Notice both answers equal 23,053,525

With that explanation out of the way, let's continue. Next, we take the number 23,053,525 and divide it by 2:

23,053,525 ÷ 2 = 11,526,762.5

If the quotient is a whole number, then 2 and 11,526,762.5 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 23,053,525
-1 -23,053,525

Now, we try dividing 23,053,525 by 3:

23,053,525 ÷ 3 = 7,684,508.3333

If the quotient is a whole number, then 3 and 7,684,508.3333 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 23,053,525
-1 -23,053,525

Let's try dividing by 4:

23,053,525 ÷ 4 = 5,763,381.25

If the quotient is a whole number, then 4 and 5,763,381.25 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 23,053,525
-1 23,053,525
Keep dividing by the next highest number until you cannot divide anymore.

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

151125551212756053,0257,62138,10583,831190,525419,155922,1412,095,7754,610,70523,053,525
-1-5-11-25-55-121-275-605-3,025-7,621-38,105-83,831-190,525-419,155-922,141-2,095,775-4,610,705-23,053,525

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