Q: What are the factor combinations of the number 2,144,017?

 A:
Positive:   1 x 214401719 x 112843
Negative: -1 x -2144017-19 x -112843


How do I find the factor combinations of the number 2,144,017?

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 2,144,017, 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 2,144,017
-1 -2,144,017

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 2,144,017.

Example:
1 x 2,144,017 = 2,144,017
and
-1 x -2,144,017 = 2,144,017
Notice both answers equal 2,144,017

With that explanation out of the way, let's continue. Next, we take the number 2,144,017 and divide it by 2:

2,144,017 ÷ 2 = 1,072,008.5

If the quotient is a whole number, then 2 and 1,072,008.5 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 2,144,017
-1 -2,144,017

Now, we try dividing 2,144,017 by 3:

2,144,017 ÷ 3 = 714,672.3333

If the quotient is a whole number, then 3 and 714,672.3333 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 2,144,017
-1 -2,144,017

Let's try dividing by 4:

2,144,017 ÷ 4 = 536,004.25

If the quotient is a whole number, then 4 and 536,004.25 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 2,144,017
-1 2,144,017
Keep dividing by the next highest number until you cannot divide anymore.

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

119112,8432,144,017
-1-19-112,843-2,144,017

More Examples

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