Q: What are the factor combinations of the number 260,513?

 A:
Positive:   1 x 26051311 x 23683121 x 2153
Negative: -1 x -260513-11 x -23683-121 x -2153


How do I find the factor combinations of the number 260,513?

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 260,513, 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.

1 260,513
-1 -260,513

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 260,513.

Example:
1 x 260,513 = 260,513
and
-1 x -260,513 = 260,513
Notice both answers equal 260,513

With that explanation out of the way, let's continue. Next, we take the number 260,513 and divide it by 2:

260,513 ÷ 2 = 130,256.5

If the quotient is a whole number, then 2 and 130,256.5 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:

1 260,513
-1 -260,513

Now, we try dividing 260,513 by 3:

260,513 ÷ 3 = 86,837.6667

If the quotient is a whole number, then 3 and 86,837.6667 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:

1 260,513
-1 -260,513

Let's try dividing by 4:

260,513 ÷ 4 = 65,128.25

If the quotient is a whole number, then 4 and 65,128.25 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:

1 260,513
-1 260,513
Keep dividing by the next highest number until you cannot divide anymore.

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

1111212,15323,683260,513
-1-11-121-2,153-23,683-260,513

More Examples

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