Q: What are the factor combinations of the number 315,875?

 A:
Positive:   1 x 3158755 x 631757 x 4512519 x 1662525 x 1263535 x 902595 x 3325125 x 2527133 x 2375175 x 1805361 x 875475 x 665
Negative: -1 x -315875-5 x -63175-7 x -45125-19 x -16625-25 x -12635-35 x -9025-95 x -3325-125 x -2527-133 x -2375-175 x -1805-361 x -875-475 x -665


How do I find the factor combinations of the number 315,875?

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 315,875, 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.

1 315,875
-1 -315,875

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 315,875.

Example:
1 x 315,875 = 315,875
and
-1 x -315,875 = 315,875
Notice both answers equal 315,875

With that explanation out of the way, let's continue. Next, we take the number 315,875 and divide it by 2:

315,875 ÷ 2 = 157,937.5

If the quotient is a whole number, then 2 and 157,937.5 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:

1 315,875
-1 -315,875

Now, we try dividing 315,875 by 3:

315,875 ÷ 3 = 105,291.6667

If the quotient is a whole number, then 3 and 105,291.6667 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:

1 315,875
-1 -315,875

Let's try dividing by 4:

315,875 ÷ 4 = 78,968.75

If the quotient is a whole number, then 4 and 78,968.75 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:

1 315,875
-1 315,875
Keep dividing by the next highest number until you cannot divide anymore.

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

157192535951251331753614756658751,8052,3752,5273,3259,02512,63516,62545,12563,175315,875
-1-5-7-19-25-35-95-125-133-175-361-475-665-875-1,805-2,375-2,527-3,325-9,025-12,635-16,625-45,125-63,175-315,875

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