Q: What are the factor combinations of the number 508,865?

 A:
Positive:   1 x 5088655 x 1017737 x 7269531 x 1641535 x 1453949 x 1038567 x 7595155 x 3283217 x 2345245 x 2077335 x 1519469 x 1085
Negative: -1 x -508865-5 x -101773-7 x -72695-31 x -16415-35 x -14539-49 x -10385-67 x -7595-155 x -3283-217 x -2345-245 x -2077-335 x -1519-469 x -1085


How do I find the factor combinations of the number 508,865?

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 508,865, 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.

1 508,865
-1 -508,865

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 508,865.

Example:
1 x 508,865 = 508,865
and
-1 x -508,865 = 508,865
Notice both answers equal 508,865

With that explanation out of the way, let's continue. Next, we take the number 508,865 and divide it by 2:

508,865 ÷ 2 = 254,432.5

If the quotient is a whole number, then 2 and 254,432.5 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:

1 508,865
-1 -508,865

Now, we try dividing 508,865 by 3:

508,865 ÷ 3 = 169,621.6667

If the quotient is a whole number, then 3 and 169,621.6667 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:

1 508,865
-1 -508,865

Let's try dividing by 4:

508,865 ÷ 4 = 127,216.25

If the quotient is a whole number, then 4 and 127,216.25 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:

1 508,865
-1 508,865
Keep dividing by the next highest number until you cannot divide anymore.

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

157313549671552172453354691,0851,5192,0772,3453,2837,59510,38514,53916,41572,695101,773508,865
-1-5-7-31-35-49-67-155-217-245-335-469-1,085-1,519-2,077-2,345-3,283-7,595-10,385-14,539-16,415-72,695-101,773-508,865

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