Q: What are the factor combinations of the number 781,625?

 A:
Positive:   1 x 7816255 x 15632513 x 6012525 x 3126537 x 2112565 x 12025125 x 6253169 x 4625185 x 4225325 x 2405481 x 1625845 x 925
Negative: -1 x -781625-5 x -156325-13 x -60125-25 x -31265-37 x -21125-65 x -12025-125 x -6253-169 x -4625-185 x -4225-325 x -2405-481 x -1625-845 x -925


How do I find the factor combinations of the number 781,625?

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 781,625, 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.

1 781,625
-1 -781,625

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 781,625.

Example:
1 x 781,625 = 781,625
and
-1 x -781,625 = 781,625
Notice both answers equal 781,625

With that explanation out of the way, let's continue. Next, we take the number 781,625 and divide it by 2:

781,625 ÷ 2 = 390,812.5

If the quotient is a whole number, then 2 and 390,812.5 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:

1 781,625
-1 -781,625

Now, we try dividing 781,625 by 3:

781,625 ÷ 3 = 260,541.6667

If the quotient is a whole number, then 3 and 260,541.6667 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:

1 781,625
-1 -781,625

Let's try dividing by 4:

781,625 ÷ 4 = 195,406.25

If the quotient is a whole number, then 4 and 195,406.25 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:

1 781,625
-1 781,625
Keep dividing by the next highest number until you cannot divide anymore.

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

15132537651251691853254818459251,6252,4054,2254,6256,25312,02521,12531,26560,125156,325781,625
-1-5-13-25-37-65-125-169-185-325-481-845-925-1,625-2,405-4,225-4,625-6,253-12,025-21,125-31,265-60,125-156,325-781,625

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