Q: What are the factor combinations of the number 10,238,131?

 A:
Positive:   1 x 1023813117 x 60224319 x 53884929 x 353039323 x 31697493 x 20767551 x 185811093 x 9367
Negative: -1 x -10238131-17 x -602243-19 x -538849-29 x -353039-323 x -31697-493 x -20767-551 x -18581-1093 x -9367


How do I find the factor combinations of the number 10,238,131?

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 10,238,131, 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 10,238,131
-1 -10,238,131

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 10,238,131.

Example:
1 x 10,238,131 = 10,238,131
and
-1 x -10,238,131 = 10,238,131
Notice both answers equal 10,238,131

With that explanation out of the way, let's continue. Next, we take the number 10,238,131 and divide it by 2:

10,238,131 ÷ 2 = 5,119,065.5

If the quotient is a whole number, then 2 and 5,119,065.5 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 10,238,131
-1 -10,238,131

Now, we try dividing 10,238,131 by 3:

10,238,131 ÷ 3 = 3,412,710.3333

If the quotient is a whole number, then 3 and 3,412,710.3333 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 10,238,131
-1 -10,238,131

Let's try dividing by 4:

10,238,131 ÷ 4 = 2,559,532.75

If the quotient is a whole number, then 4 and 2,559,532.75 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 10,238,131
-1 10,238,131
Keep dividing by the next highest number until you cannot divide anymore.

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

11719293234935511,0939,36718,58120,76731,697353,039538,849602,24310,238,131
-1-17-19-29-323-493-551-1,093-9,367-18,581-20,767-31,697-353,039-538,849-602,243-10,238,131

More Examples

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