Q: What are the factor combinations of the number 210,376,849?

 A:
Positive:   1 x 210376849373 x 564013
Negative: -1 x -210376849-373 x -564013


How do I find the factor combinations of the number 210,376,849?

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 210,376,849, 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.

1 210,376,849
-1 -210,376,849

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 210,376,849.

Example:
1 x 210,376,849 = 210,376,849
and
-1 x -210,376,849 = 210,376,849
Notice both answers equal 210,376,849

With that explanation out of the way, let's continue. Next, we take the number 210,376,849 and divide it by 2:

210,376,849 ÷ 2 = 105,188,424.5

If the quotient is a whole number, then 2 and 105,188,424.5 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:

1 210,376,849
-1 -210,376,849

Now, we try dividing 210,376,849 by 3:

210,376,849 ÷ 3 = 70,125,616.3333

If the quotient is a whole number, then 3 and 70,125,616.3333 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:

1 210,376,849
-1 -210,376,849

Let's try dividing by 4:

210,376,849 ÷ 4 = 52,594,212.25

If the quotient is a whole number, then 4 and 52,594,212.25 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:

1 210,376,849
-1 210,376,849
Keep dividing by the next highest number until you cannot divide anymore.

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

1373564,013210,376,849
-1-373-564,013-210,376,849

More Examples

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