Q: What are the factor combinations of the number 812,725?

 A:
Positive:   1 x 8127255 x 16254519 x 4277525 x 3250929 x 2802559 x 1377595 x 8555145 x 5605295 x 2755475 x 1711551 x 1475725 x 1121
Negative: -1 x -812725-5 x -162545-19 x -42775-25 x -32509-29 x -28025-59 x -13775-95 x -8555-145 x -5605-295 x -2755-475 x -1711-551 x -1475-725 x -1121


How do I find the factor combinations of the number 812,725?

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 812,725, 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.

1 812,725
-1 -812,725

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 812,725.

Example:
1 x 812,725 = 812,725
and
-1 x -812,725 = 812,725
Notice both answers equal 812,725

With that explanation out of the way, let's continue. Next, we take the number 812,725 and divide it by 2:

812,725 ÷ 2 = 406,362.5

If the quotient is a whole number, then 2 and 406,362.5 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:

1 812,725
-1 -812,725

Now, we try dividing 812,725 by 3:

812,725 ÷ 3 = 270,908.3333

If the quotient is a whole number, then 3 and 270,908.3333 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:

1 812,725
-1 -812,725

Let's try dividing by 4:

812,725 ÷ 4 = 203,181.25

If the quotient is a whole number, then 4 and 203,181.25 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:

1 812,725
-1 812,725
Keep dividing by the next highest number until you cannot divide anymore.

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

1519252959951452954755517251,1211,4751,7112,7555,6058,55513,77528,02532,50942,775162,545812,725
-1-5-19-25-29-59-95-145-295-475-551-725-1,121-1,475-1,711-2,755-5,605-8,555-13,775-28,025-32,509-42,775-162,545-812,725

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