Q: What are the factor combinations of the number 3,412,625?

 A:
Positive:   1 x 34126255 x 68252523 x 14837525 x 136505115 x 29675125 x 27301575 x 59351187 x 2875
Negative: -1 x -3412625-5 x -682525-23 x -148375-25 x -136505-115 x -29675-125 x -27301-575 x -5935-1187 x -2875


How do I find the factor combinations of the number 3,412,625?

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 3,412,625, 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 3,412,625
-1 -3,412,625

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 3,412,625.

Example:
1 x 3,412,625 = 3,412,625
and
-1 x -3,412,625 = 3,412,625
Notice both answers equal 3,412,625

With that explanation out of the way, let's continue. Next, we take the number 3,412,625 and divide it by 2:

3,412,625 ÷ 2 = 1,706,312.5

If the quotient is a whole number, then 2 and 1,706,312.5 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 3,412,625
-1 -3,412,625

Now, we try dividing 3,412,625 by 3:

3,412,625 ÷ 3 = 1,137,541.6667

If the quotient is a whole number, then 3 and 1,137,541.6667 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 3,412,625
-1 -3,412,625

Let's try dividing by 4:

3,412,625 ÷ 4 = 853,156.25

If the quotient is a whole number, then 4 and 853,156.25 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 3,412,625
-1 3,412,625
Keep dividing by the next highest number until you cannot divide anymore.

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

1523251151255751,1872,8755,93527,30129,675136,505148,375682,5253,412,625
-1-5-23-25-115-125-575-1,187-2,875-5,935-27,301-29,675-136,505-148,375-682,525-3,412,625

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