Q: What are the factor combinations of the number 27,633,617?

 A:
Positive:   1 x 2763361711 x 251214731 x 89140753 x 521389121 x 228377139 x 198803341 x 81037583 x 473991529 x 180731643 x 168193751 x 73674309 x 6413
Negative: -1 x -27633617-11 x -2512147-31 x -891407-53 x -521389-121 x -228377-139 x -198803-341 x -81037-583 x -47399-1529 x -18073-1643 x -16819-3751 x -7367-4309 x -6413


How do I find the factor combinations of the number 27,633,617?

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 27,633,617, 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 27,633,617
-1 -27,633,617

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 27,633,617.

Example:
1 x 27,633,617 = 27,633,617
and
-1 x -27,633,617 = 27,633,617
Notice both answers equal 27,633,617

With that explanation out of the way, let's continue. Next, we take the number 27,633,617 and divide it by 2:

27,633,617 ÷ 2 = 13,816,808.5

If the quotient is a whole number, then 2 and 13,816,808.5 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 27,633,617
-1 -27,633,617

Now, we try dividing 27,633,617 by 3:

27,633,617 ÷ 3 = 9,211,205.6667

If the quotient is a whole number, then 3 and 9,211,205.6667 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 27,633,617
-1 -27,633,617

Let's try dividing by 4:

27,633,617 ÷ 4 = 6,908,404.25

If the quotient is a whole number, then 4 and 6,908,404.25 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 27,633,617
-1 27,633,617
Keep dividing by the next highest number until you cannot divide anymore.

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

11131531211393415831,5291,6433,7514,3096,4137,36716,81918,07347,39981,037198,803228,377521,389891,4072,512,14727,633,617
-1-11-31-53-121-139-341-583-1,529-1,643-3,751-4,309-6,413-7,367-16,819-18,073-47,399-81,037-198,803-228,377-521,389-891,407-2,512,147-27,633,617

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