Q: What are the factor combinations of the number 59,213?

 A:
Positive:   1 x 592137 x 845911 x 538377 x 769
Negative: -1 x -59213-7 x -8459-11 x -5383-77 x -769


How do I find the factor combinations of the number 59,213?

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 59,213, 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 59,213
-1 -59,213

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 59,213.

Example:
1 x 59,213 = 59,213
and
-1 x -59,213 = 59,213
Notice both answers equal 59,213

With that explanation out of the way, let's continue. Next, we take the number 59,213 and divide it by 2:

59,213 ÷ 2 = 29,606.5

If the quotient is a whole number, then 2 and 29,606.5 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 59,213
-1 -59,213

Now, we try dividing 59,213 by 3:

59,213 ÷ 3 = 19,737.6667

If the quotient is a whole number, then 3 and 19,737.6667 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 59,213
-1 -59,213

Let's try dividing by 4:

59,213 ÷ 4 = 14,803.25

If the quotient is a whole number, then 4 and 14,803.25 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 59,213
-1 59,213
Keep dividing by the next highest number until you cannot divide anymore.

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

1711777695,3838,45959,213
-1-7-11-77-769-5,383-8,459-59,213

More Examples

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