Q: What are the factor combinations of the number 353,597?

 A:
Positive:   1 x 35359729 x 1219389 x 3973137 x 2581
Negative: -1 x -353597-29 x -12193-89 x -3973-137 x -2581


How do I find the factor combinations of the number 353,597?

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 353,597, 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.

1 353,597
-1 -353,597

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 353,597.

Example:
1 x 353,597 = 353,597
and
-1 x -353,597 = 353,597
Notice both answers equal 353,597

With that explanation out of the way, let's continue. Next, we take the number 353,597 and divide it by 2:

353,597 ÷ 2 = 176,798.5

If the quotient is a whole number, then 2 and 176,798.5 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:

1 353,597
-1 -353,597

Now, we try dividing 353,597 by 3:

353,597 ÷ 3 = 117,865.6667

If the quotient is a whole number, then 3 and 117,865.6667 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:

1 353,597
-1 -353,597

Let's try dividing by 4:

353,597 ÷ 4 = 88,399.25

If the quotient is a whole number, then 4 and 88,399.25 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:

1 353,597
-1 353,597
Keep dividing by the next highest number until you cannot divide anymore.

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

129891372,5813,97312,193353,597
-1-29-89-137-2,581-3,973-12,193-353,597

More Examples

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