Q: What are the factor combinations of the number 42,003,103?

 A:
Positive:   1 x 4200310337 x 113521959 x 71191771 x 591593271 x 1549932183 x 192412627 x 159894189 x 10027
Negative: -1 x -42003103-37 x -1135219-59 x -711917-71 x -591593-271 x -154993-2183 x -19241-2627 x -15989-4189 x -10027


How do I find the factor combinations of the number 42,003,103?

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 42,003,103, 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 42,003,103
-1 -42,003,103

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 42,003,103.

Example:
1 x 42,003,103 = 42,003,103
and
-1 x -42,003,103 = 42,003,103
Notice both answers equal 42,003,103

With that explanation out of the way, let's continue. Next, we take the number 42,003,103 and divide it by 2:

42,003,103 ÷ 2 = 21,001,551.5

If the quotient is a whole number, then 2 and 21,001,551.5 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 42,003,103
-1 -42,003,103

Now, we try dividing 42,003,103 by 3:

42,003,103 ÷ 3 = 14,001,034.3333

If the quotient is a whole number, then 3 and 14,001,034.3333 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 42,003,103
-1 -42,003,103

Let's try dividing by 4:

42,003,103 ÷ 4 = 10,500,775.75

If the quotient is a whole number, then 4 and 10,500,775.75 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 42,003,103
-1 42,003,103
Keep dividing by the next highest number until you cannot divide anymore.

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

13759712712,1832,6274,18910,02715,98919,241154,993591,593711,9171,135,21942,003,103
-1-37-59-71-271-2,183-2,627-4,189-10,027-15,989-19,241-154,993-591,593-711,917-1,135,219-42,003,103

More Examples

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