Q: What are the factor combinations of the number 8,417,125?

 A:
Positive:   1 x 84171255 x 168342517 x 49512525 x 33668585 x 99025125 x 67337233 x 36125289 x 29125425 x 198051165 x 72251445 x 58252125 x 3961
Negative: -1 x -8417125-5 x -1683425-17 x -495125-25 x -336685-85 x -99025-125 x -67337-233 x -36125-289 x -29125-425 x -19805-1165 x -7225-1445 x -5825-2125 x -3961


How do I find the factor combinations of the number 8,417,125?

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 8,417,125, 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 8,417,125
-1 -8,417,125

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 8,417,125.

Example:
1 x 8,417,125 = 8,417,125
and
-1 x -8,417,125 = 8,417,125
Notice both answers equal 8,417,125

With that explanation out of the way, let's continue. Next, we take the number 8,417,125 and divide it by 2:

8,417,125 ÷ 2 = 4,208,562.5

If the quotient is a whole number, then 2 and 4,208,562.5 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 8,417,125
-1 -8,417,125

Now, we try dividing 8,417,125 by 3:

8,417,125 ÷ 3 = 2,805,708.3333

If the quotient is a whole number, then 3 and 2,805,708.3333 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 8,417,125
-1 -8,417,125

Let's try dividing by 4:

8,417,125 ÷ 4 = 2,104,281.25

If the quotient is a whole number, then 4 and 2,104,281.25 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 8,417,125
-1 8,417,125
Keep dividing by the next highest number until you cannot divide anymore.

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

151725851252332894251,1651,4452,1253,9615,8257,22519,80529,12536,12567,33799,025336,685495,1251,683,4258,417,125
-1-5-17-25-85-125-233-289-425-1,165-1,445-2,125-3,961-5,825-7,225-19,805-29,125-36,125-67,337-99,025-336,685-495,125-1,683,425-8,417,125

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