Q: What are the factor combinations of the number 210,708?

 A:
Positive:   1 x 2107082 x 1053543 x 702364 x 526776 x 351189 x 2341212 x 1755918 x 1170627 x 780436 x 585354 x 3902108 x 1951
Negative: -1 x -210708-2 x -105354-3 x -70236-4 x -52677-6 x -35118-9 x -23412-12 x -17559-18 x -11706-27 x -7804-36 x -5853-54 x -3902-108 x -1951


How do I find the factor combinations of the number 210,708?

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 210,708, 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.

1 210,708
-1 -210,708

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 210,708.

Example:
1 x 210,708 = 210,708
and
-1 x -210,708 = 210,708
Notice both answers equal 210,708

With that explanation out of the way, let's continue. Next, we take the number 210,708 and divide it by 2:

210,708 ÷ 2 = 105,354

If the quotient is a whole number, then 2 and 105,354 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 105,354 210,708
-1 -2 -105,354 -210,708

Now, we try dividing 210,708 by 3:

210,708 ÷ 3 = 70,236

If the quotient is a whole number, then 3 and 70,236 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 70,236 105,354 210,708
-1 -2 -3 -70,236 -105,354 -210,708

Let's try dividing by 4:

210,708 ÷ 4 = 52,677

If the quotient is a whole number, then 4 and 52,677 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 52,677 70,236 105,354 210,708
-1 -2 -3 -4 -52,677 -70,236 -105,354 210,708
Keep dividing by the next highest number until you cannot divide anymore.

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

12346912182736541081,9513,9025,8537,80411,70617,55923,41235,11852,67770,236105,354210,708
-1-2-3-4-6-9-12-18-27-36-54-108-1,951-3,902-5,853-7,804-11,706-17,559-23,412-35,118-52,677-70,236-105,354-210,708

More Examples

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