Q: What are the factor combinations of the number 214,613?

 A:
Positive:   1 x 2146137 x 3065923 x 933131 x 692343 x 4991161 x 1333217 x 989301 x 713
Negative: -1 x -214613-7 x -30659-23 x -9331-31 x -6923-43 x -4991-161 x -1333-217 x -989-301 x -713


How do I find the factor combinations of the number 214,613?

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 214,613, 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.

1 214,613
-1 -214,613

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 214,613.

Example:
1 x 214,613 = 214,613
and
-1 x -214,613 = 214,613
Notice both answers equal 214,613

With that explanation out of the way, let's continue. Next, we take the number 214,613 and divide it by 2:

214,613 ÷ 2 = 107,306.5

If the quotient is a whole number, then 2 and 107,306.5 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:

1 214,613
-1 -214,613

Now, we try dividing 214,613 by 3:

214,613 ÷ 3 = 71,537.6667

If the quotient is a whole number, then 3 and 71,537.6667 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:

1 214,613
-1 -214,613

Let's try dividing by 4:

214,613 ÷ 4 = 53,653.25

If the quotient is a whole number, then 4 and 53,653.25 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:

1 214,613
-1 214,613
Keep dividing by the next highest number until you cannot divide anymore.

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

172331431612173017139891,3334,9916,9239,33130,659214,613
-1-7-23-31-43-161-217-301-713-989-1,333-4,991-6,923-9,331-30,659-214,613

More Examples

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