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

 A:
Positive:   1 x 12310303319 x 647910737 x 332710941 x 3002513703 x 175111779 x 1580271517 x 811494271 x 28823
Negative: -1 x -123103033-19 x -6479107-37 x -3327109-41 x -3002513-703 x -175111-779 x -158027-1517 x -81149-4271 x -28823


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

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 123,103,033, 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.

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

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 123,103,033.

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

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

123,103,033 ÷ 2 = 61,551,516.5

If the quotient is a whole number, then 2 and 61,551,516.5 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:

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

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

123,103,033 ÷ 3 = 41,034,344.3333

If the quotient is a whole number, then 3 and 41,034,344.3333 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:

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

Let's try dividing by 4:

123,103,033 ÷ 4 = 30,775,758.25

If the quotient is a whole number, then 4 and 30,775,758.25 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:

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

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

11937417037791,5174,27128,82381,149158,027175,1113,002,5133,327,1096,479,107123,103,033
-1-19-37-41-703-779-1,517-4,271-28,823-81,149-158,027-175,111-3,002,513-3,327,109-6,479,107-123,103,033

More Examples

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