Q: What are the factor combinations of the number 321,105,325?

 A:
Positive:   1 x 3211053255 x 6422106525 x 1284421389 x 3607925277 x 1159225445 x 721585521 x 6163251385 x 2318452225 x 1443172605 x 1232656925 x 4636913025 x 24653
Negative: -1 x -321105325-5 x -64221065-25 x -12844213-89 x -3607925-277 x -1159225-445 x -721585-521 x -616325-1385 x -231845-2225 x -144317-2605 x -123265-6925 x -46369-13025 x -24653


How do I find the factor combinations of the number 321,105,325?

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 321,105,325, 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.

1 321,105,325
-1 -321,105,325

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 321,105,325.

Example:
1 x 321,105,325 = 321,105,325
and
-1 x -321,105,325 = 321,105,325
Notice both answers equal 321,105,325

With that explanation out of the way, let's continue. Next, we take the number 321,105,325 and divide it by 2:

321,105,325 ÷ 2 = 160,552,662.5

If the quotient is a whole number, then 2 and 160,552,662.5 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:

1 321,105,325
-1 -321,105,325

Now, we try dividing 321,105,325 by 3:

321,105,325 ÷ 3 = 107,035,108.3333

If the quotient is a whole number, then 3 and 107,035,108.3333 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:

1 321,105,325
-1 -321,105,325

Let's try dividing by 4:

321,105,325 ÷ 4 = 80,276,331.25

If the quotient is a whole number, then 4 and 80,276,331.25 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:

1 321,105,325
-1 321,105,325
Keep dividing by the next highest number until you cannot divide anymore.

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

1525892774455211,3852,2252,6056,92513,02524,65346,369123,265144,317231,845616,325721,5851,159,2253,607,92512,844,21364,221,065321,105,325
-1-5-25-89-277-445-521-1,385-2,225-2,605-6,925-13,025-24,653-46,369-123,265-144,317-231,845-616,325-721,585-1,159,225-3,607,925-12,844,213-64,221,065-321,105,325

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