Q: What are the factor combinations of the number 677,075?

 A:
Positive:   1 x 6770755 x 1354157 x 9672525 x 2708335 x 1934553 x 1277573 x 9275175 x 3869265 x 2555365 x 1855371 x 1825511 x 1325
Negative: -1 x -677075-5 x -135415-7 x -96725-25 x -27083-35 x -19345-53 x -12775-73 x -9275-175 x -3869-265 x -2555-365 x -1855-371 x -1825-511 x -1325


How do I find the factor combinations of the number 677,075?

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 677,075, 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.

1 677,075
-1 -677,075

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 677,075.

Example:
1 x 677,075 = 677,075
and
-1 x -677,075 = 677,075
Notice both answers equal 677,075

With that explanation out of the way, let's continue. Next, we take the number 677,075 and divide it by 2:

677,075 ÷ 2 = 338,537.5

If the quotient is a whole number, then 2 and 338,537.5 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:

1 677,075
-1 -677,075

Now, we try dividing 677,075 by 3:

677,075 ÷ 3 = 225,691.6667

If the quotient is a whole number, then 3 and 225,691.6667 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:

1 677,075
-1 -677,075

Let's try dividing by 4:

677,075 ÷ 4 = 169,268.75

If the quotient is a whole number, then 4 and 169,268.75 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:

1 677,075
-1 677,075
Keep dividing by the next highest number until you cannot divide anymore.

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

157253553731752653653715111,3251,8251,8552,5553,8699,27512,77519,34527,08396,725135,415677,075
-1-5-7-25-35-53-73-175-265-365-371-511-1,325-1,825-1,855-2,555-3,869-9,275-12,775-19,345-27,083-96,725-135,415-677,075

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