Q: What are the factor combinations of the number 410,375?

 A:
Positive:   1 x 4103755 x 820757 x 5862525 x 1641535 x 1172549 x 837567 x 6125125 x 3283175 x 2345245 x 1675335 x 1225469 x 875
Negative: -1 x -410375-5 x -82075-7 x -58625-25 x -16415-35 x -11725-49 x -8375-67 x -6125-125 x -3283-175 x -2345-245 x -1675-335 x -1225-469 x -875


How do I find the factor combinations of the number 410,375?

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 410,375, 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.

1 410,375
-1 -410,375

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 410,375.

Example:
1 x 410,375 = 410,375
and
-1 x -410,375 = 410,375
Notice both answers equal 410,375

With that explanation out of the way, let's continue. Next, we take the number 410,375 and divide it by 2:

410,375 ÷ 2 = 205,187.5

If the quotient is a whole number, then 2 and 205,187.5 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:

1 410,375
-1 -410,375

Now, we try dividing 410,375 by 3:

410,375 ÷ 3 = 136,791.6667

If the quotient is a whole number, then 3 and 136,791.6667 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:

1 410,375
-1 -410,375

Let's try dividing by 4:

410,375 ÷ 4 = 102,593.75

If the quotient is a whole number, then 4 and 102,593.75 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:

1 410,375
-1 410,375
Keep dividing by the next highest number until you cannot divide anymore.

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

157253549671251752453354698751,2251,6752,3453,2836,1258,37511,72516,41558,62582,075410,375
-1-5-7-25-35-49-67-125-175-245-335-469-875-1,225-1,675-2,345-3,283-6,125-8,375-11,725-16,415-58,625-82,075-410,375

More Examples

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