Q: What are the factor combinations of the number 35,003?

 A:
Positive:   1 x 3500317 x 205929 x 120771 x 493
Negative: -1 x -35003-17 x -2059-29 x -1207-71 x -493


How do I find the factor combinations of the number 35,003?

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 35,003, 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 35,003
-1 -35,003

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 35,003.

Example:
1 x 35,003 = 35,003
and
-1 x -35,003 = 35,003
Notice both answers equal 35,003

With that explanation out of the way, let's continue. Next, we take the number 35,003 and divide it by 2:

35,003 ÷ 2 = 17,501.5

If the quotient is a whole number, then 2 and 17,501.5 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 35,003
-1 -35,003

Now, we try dividing 35,003 by 3:

35,003 ÷ 3 = 11,667.6667

If the quotient is a whole number, then 3 and 11,667.6667 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 35,003
-1 -35,003

Let's try dividing by 4:

35,003 ÷ 4 = 8,750.75

If the quotient is a whole number, then 4 and 8,750.75 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 35,003
-1 35,003
Keep dividing by the next highest number until you cannot divide anymore.

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

11729714931,2072,05935,003
-1-17-29-71-493-1,207-2,059-35,003

More Examples

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