Q: What are the factor combinations of the number 110,431,529?

 A:
Positive:   1 x 11043152913 x 849473347 x 2349607169 x 653441611 x 1807397943 x 13903
Negative: -1 x -110431529-13 x -8494733-47 x -2349607-169 x -653441-611 x -180739-7943 x -13903


How do I find the factor combinations of the number 110,431,529?

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 110,431,529, 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.

1 110,431,529
-1 -110,431,529

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 110,431,529.

Example:
1 x 110,431,529 = 110,431,529
and
-1 x -110,431,529 = 110,431,529
Notice both answers equal 110,431,529

With that explanation out of the way, let's continue. Next, we take the number 110,431,529 and divide it by 2:

110,431,529 ÷ 2 = 55,215,764.5

If the quotient is a whole number, then 2 and 55,215,764.5 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:

1 110,431,529
-1 -110,431,529

Now, we try dividing 110,431,529 by 3:

110,431,529 ÷ 3 = 36,810,509.6667

If the quotient is a whole number, then 3 and 36,810,509.6667 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:

1 110,431,529
-1 -110,431,529

Let's try dividing by 4:

110,431,529 ÷ 4 = 27,607,882.25

If the quotient is a whole number, then 4 and 27,607,882.25 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:

1 110,431,529
-1 110,431,529
Keep dividing by the next highest number until you cannot divide anymore.

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

113471696117,94313,903180,739653,4412,349,6078,494,733110,431,529
-1-13-47-169-611-7,943-13,903-180,739-653,441-2,349,607-8,494,733-110,431,529

More Examples

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