Q: What are the factor combinations of the number 782,425?

 A:
Positive:   1 x 7824255 x 1564857 x 11177517 x 4602525 x 3129735 x 2235585 x 9205119 x 6575175 x 4471263 x 2975425 x 1841595 x 1315
Negative: -1 x -782425-5 x -156485-7 x -111775-17 x -46025-25 x -31297-35 x -22355-85 x -9205-119 x -6575-175 x -4471-263 x -2975-425 x -1841-595 x -1315


How do I find the factor combinations of the number 782,425?

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 782,425, 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.

1 782,425
-1 -782,425

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 782,425.

Example:
1 x 782,425 = 782,425
and
-1 x -782,425 = 782,425
Notice both answers equal 782,425

With that explanation out of the way, let's continue. Next, we take the number 782,425 and divide it by 2:

782,425 ÷ 2 = 391,212.5

If the quotient is a whole number, then 2 and 391,212.5 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:

1 782,425
-1 -782,425

Now, we try dividing 782,425 by 3:

782,425 ÷ 3 = 260,808.3333

If the quotient is a whole number, then 3 and 260,808.3333 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:

1 782,425
-1 -782,425

Let's try dividing by 4:

782,425 ÷ 4 = 195,606.25

If the quotient is a whole number, then 4 and 195,606.25 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:

1 782,425
-1 782,425
Keep dividing by the next highest number until you cannot divide anymore.

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

157172535851191752634255951,3151,8412,9754,4716,5759,20522,35531,29746,025111,775156,485782,425
-1-5-7-17-25-35-85-119-175-263-425-595-1,315-1,841-2,975-4,471-6,575-9,205-22,355-31,297-46,025-111,775-156,485-782,425

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