Q: What are the factor combinations of the number 23,123,035?

 A:
Positive:   1 x 231230355 x 462460713 x 177869543 x 53774565 x 355739215 x 107549559 x 413652795 x 8273
Negative: -1 x -23123035-5 x -4624607-13 x -1778695-43 x -537745-65 x -355739-215 x -107549-559 x -41365-2795 x -8273


How do I find the factor combinations of the number 23,123,035?

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 23,123,035, 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 23,123,035
-1 -23,123,035

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 23,123,035.

Example:
1 x 23,123,035 = 23,123,035
and
-1 x -23,123,035 = 23,123,035
Notice both answers equal 23,123,035

With that explanation out of the way, let's continue. Next, we take the number 23,123,035 and divide it by 2:

23,123,035 ÷ 2 = 11,561,517.5

If the quotient is a whole number, then 2 and 11,561,517.5 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 23,123,035
-1 -23,123,035

Now, we try dividing 23,123,035 by 3:

23,123,035 ÷ 3 = 7,707,678.3333

If the quotient is a whole number, then 3 and 7,707,678.3333 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 23,123,035
-1 -23,123,035

Let's try dividing by 4:

23,123,035 ÷ 4 = 5,780,758.75

If the quotient is a whole number, then 4 and 5,780,758.75 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 23,123,035
-1 23,123,035
Keep dividing by the next highest number until you cannot divide anymore.

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

151343652155592,7958,27341,365107,549355,739537,7451,778,6954,624,60723,123,035
-1-5-13-43-65-215-559-2,795-8,273-41,365-107,549-355,739-537,745-1,778,695-4,624,607-23,123,035

More Examples

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