Q: What are the factor combinations of the number 710,215?

 A:
Positive:   1 x 7102155 x 14204311 x 6456537 x 1919555 x 12913185 x 3839349 x 2035407 x 1745
Negative: -1 x -710215-5 x -142043-11 x -64565-37 x -19195-55 x -12913-185 x -3839-349 x -2035-407 x -1745


How do I find the factor combinations of the number 710,215?

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 710,215, 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.

1 710,215
-1 -710,215

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 710,215.

Example:
1 x 710,215 = 710,215
and
-1 x -710,215 = 710,215
Notice both answers equal 710,215

With that explanation out of the way, let's continue. Next, we take the number 710,215 and divide it by 2:

710,215 ÷ 2 = 355,107.5

If the quotient is a whole number, then 2 and 355,107.5 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:

1 710,215
-1 -710,215

Now, we try dividing 710,215 by 3:

710,215 ÷ 3 = 236,738.3333

If the quotient is a whole number, then 3 and 236,738.3333 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:

1 710,215
-1 -710,215

Let's try dividing by 4:

710,215 ÷ 4 = 177,553.75

If the quotient is a whole number, then 4 and 177,553.75 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:

1 710,215
-1 710,215
Keep dividing by the next highest number until you cannot divide anymore.

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

151137551853494071,7452,0353,83912,91319,19564,565142,043710,215
-1-5-11-37-55-185-349-407-1,745-2,035-3,839-12,913-19,195-64,565-142,043-710,215

More Examples

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