Q: What are the factor combinations of the number 10,404,251?

 A:
Positive:   1 x 1040425111 x 94584113 x 80032731 x 335621143 x 72757341 x 30511403 x 258172347 x 4433
Negative: -1 x -10404251-11 x -945841-13 x -800327-31 x -335621-143 x -72757-341 x -30511-403 x -25817-2347 x -4433


How do I find the factor combinations of the number 10,404,251?

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 10,404,251, 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 10,404,251
-1 -10,404,251

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 10,404,251.

Example:
1 x 10,404,251 = 10,404,251
and
-1 x -10,404,251 = 10,404,251
Notice both answers equal 10,404,251

With that explanation out of the way, let's continue. Next, we take the number 10,404,251 and divide it by 2:

10,404,251 ÷ 2 = 5,202,125.5

If the quotient is a whole number, then 2 and 5,202,125.5 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 10,404,251
-1 -10,404,251

Now, we try dividing 10,404,251 by 3:

10,404,251 ÷ 3 = 3,468,083.6667

If the quotient is a whole number, then 3 and 3,468,083.6667 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 10,404,251
-1 -10,404,251

Let's try dividing by 4:

10,404,251 ÷ 4 = 2,601,062.75

If the quotient is a whole number, then 4 and 2,601,062.75 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 10,404,251
-1 10,404,251
Keep dividing by the next highest number until you cannot divide anymore.

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

11113311433414032,3474,43325,81730,51172,757335,621800,327945,84110,404,251
-1-11-13-31-143-341-403-2,347-4,433-25,817-30,511-72,757-335,621-800,327-945,841-10,404,251

More Examples

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