Q: What are the factor combinations of the number 103,123,033?

 A:
Positive:   1 x 10312303313 x 793254137 x 2787109269 x 383357481 x 214393797 x 1293893497 x 294899953 x 10361
Negative: -1 x -103123033-13 x -7932541-37 x -2787109-269 x -383357-481 x -214393-797 x -129389-3497 x -29489-9953 x -10361


How do I find the factor combinations of the number 103,123,033?

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 103,123,033, 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.

1 103,123,033
-1 -103,123,033

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 103,123,033.

Example:
1 x 103,123,033 = 103,123,033
and
-1 x -103,123,033 = 103,123,033
Notice both answers equal 103,123,033

With that explanation out of the way, let's continue. Next, we take the number 103,123,033 and divide it by 2:

103,123,033 ÷ 2 = 51,561,516.5

If the quotient is a whole number, then 2 and 51,561,516.5 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:

1 103,123,033
-1 -103,123,033

Now, we try dividing 103,123,033 by 3:

103,123,033 ÷ 3 = 34,374,344.3333

If the quotient is a whole number, then 3 and 34,374,344.3333 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:

1 103,123,033
-1 -103,123,033

Let's try dividing by 4:

103,123,033 ÷ 4 = 25,780,758.25

If the quotient is a whole number, then 4 and 25,780,758.25 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:

1 103,123,033
-1 103,123,033
Keep dividing by the next highest number until you cannot divide anymore.

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

113372694817973,4979,95310,36129,489129,389214,393383,3572,787,1097,932,541103,123,033
-1-13-37-269-481-797-3,497-9,953-10,361-29,489-129,389-214,393-383,357-2,787,109-7,932,541-103,123,033

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