Q: What are the factor combinations of the number 3,109,249?

 A:
Positive:   1 x 310924911 x 28265913 x 23917317 x 182897143 x 21743187 x 16627221 x 140691279 x 2431
Negative: -1 x -3109249-11 x -282659-13 x -239173-17 x -182897-143 x -21743-187 x -16627-221 x -14069-1279 x -2431


How do I find the factor combinations of the number 3,109,249?

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 3,109,249, 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 3,109,249
-1 -3,109,249

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 3,109,249.

Example:
1 x 3,109,249 = 3,109,249
and
-1 x -3,109,249 = 3,109,249
Notice both answers equal 3,109,249

With that explanation out of the way, let's continue. Next, we take the number 3,109,249 and divide it by 2:

3,109,249 ÷ 2 = 1,554,624.5

If the quotient is a whole number, then 2 and 1,554,624.5 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 3,109,249
-1 -3,109,249

Now, we try dividing 3,109,249 by 3:

3,109,249 ÷ 3 = 1,036,416.3333

If the quotient is a whole number, then 3 and 1,036,416.3333 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 3,109,249
-1 -3,109,249

Let's try dividing by 4:

3,109,249 ÷ 4 = 777,312.25

If the quotient is a whole number, then 4 and 777,312.25 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 3,109,249
-1 3,109,249
Keep dividing by the next highest number until you cannot divide anymore.

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

11113171431872211,2792,43114,06916,62721,743182,897239,173282,6593,109,249
-1-11-13-17-143-187-221-1,279-2,431-14,069-16,627-21,743-182,897-239,173-282,659-3,109,249

More Examples

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