Q: What are the factor combinations of the number 321,475?

 A:
Positive:   1 x 3214755 x 642957 x 4592511 x 2922525 x 1285935 x 918555 x 584577 x 4175167 x 1925175 x 1837275 x 1169385 x 835
Negative: -1 x -321475-5 x -64295-7 x -45925-11 x -29225-25 x -12859-35 x -9185-55 x -5845-77 x -4175-167 x -1925-175 x -1837-275 x -1169-385 x -835


How do I find the factor combinations of the number 321,475?

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 321,475, 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.

1 321,475
-1 -321,475

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 321,475.

Example:
1 x 321,475 = 321,475
and
-1 x -321,475 = 321,475
Notice both answers equal 321,475

With that explanation out of the way, let's continue. Next, we take the number 321,475 and divide it by 2:

321,475 ÷ 2 = 160,737.5

If the quotient is a whole number, then 2 and 160,737.5 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:

1 321,475
-1 -321,475

Now, we try dividing 321,475 by 3:

321,475 ÷ 3 = 107,158.3333

If the quotient is a whole number, then 3 and 107,158.3333 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:

1 321,475
-1 -321,475

Let's try dividing by 4:

321,475 ÷ 4 = 80,368.75

If the quotient is a whole number, then 4 and 80,368.75 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:

1 321,475
-1 321,475
Keep dividing by the next highest number until you cannot divide anymore.

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

15711253555771671752753858351,1691,8371,9254,1755,8459,18512,85929,22545,92564,295321,475
-1-5-7-11-25-35-55-77-167-175-275-385-835-1,169-1,837-1,925-4,175-5,845-9,185-12,859-29,225-45,925-64,295-321,475

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