Q: What are the factor combinations of the number 710,515?

 A:
Positive:   1 x 7105155 x 14210313 x 5465517 x 4179565 x 1093185 x 8359221 x 3215643 x 1105
Negative: -1 x -710515-5 x -142103-13 x -54655-17 x -41795-65 x -10931-85 x -8359-221 x -3215-643 x -1105


How do I find the factor combinations of the number 710,515?

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 710,515, 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.

1 710,515
-1 -710,515

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 710,515.

Example:
1 x 710,515 = 710,515
and
-1 x -710,515 = 710,515
Notice both answers equal 710,515

With that explanation out of the way, let's continue. Next, we take the number 710,515 and divide it by 2:

710,515 ÷ 2 = 355,257.5

If the quotient is a whole number, then 2 and 355,257.5 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:

1 710,515
-1 -710,515

Now, we try dividing 710,515 by 3:

710,515 ÷ 3 = 236,838.3333

If the quotient is a whole number, then 3 and 236,838.3333 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:

1 710,515
-1 -710,515

Let's try dividing by 4:

710,515 ÷ 4 = 177,628.75

If the quotient is a whole number, then 4 and 177,628.75 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:

1 710,515
-1 710,515
Keep dividing by the next highest number until you cannot divide anymore.

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

15131765852216431,1053,2158,35910,93141,79554,655142,103710,515
-1-5-13-17-65-85-221-643-1,105-3,215-8,359-10,931-41,795-54,655-142,103-710,515

More Examples

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