Q: What are the factor combinations of the number 71,234,125?

 A:
Positive:   1 x 712341255 x 1424682525 x 284936531 x 2297875125 x 569873155 x 459575593 x 120125775 x 91915961 x 741252965 x 240253875 x 183834805 x 14825
Negative: -1 x -71234125-5 x -14246825-25 x -2849365-31 x -2297875-125 x -569873-155 x -459575-593 x -120125-775 x -91915-961 x -74125-2965 x -24025-3875 x -18383-4805 x -14825


How do I find the factor combinations of the number 71,234,125?

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 71,234,125, 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 71,234,125
-1 -71,234,125

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 71,234,125.

Example:
1 x 71,234,125 = 71,234,125
and
-1 x -71,234,125 = 71,234,125
Notice both answers equal 71,234,125

With that explanation out of the way, let's continue. Next, we take the number 71,234,125 and divide it by 2:

71,234,125 ÷ 2 = 35,617,062.5

If the quotient is a whole number, then 2 and 35,617,062.5 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 71,234,125
-1 -71,234,125

Now, we try dividing 71,234,125 by 3:

71,234,125 ÷ 3 = 23,744,708.3333

If the quotient is a whole number, then 3 and 23,744,708.3333 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 71,234,125
-1 -71,234,125

Let's try dividing by 4:

71,234,125 ÷ 4 = 17,808,531.25

If the quotient is a whole number, then 4 and 17,808,531.25 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 71,234,125
-1 71,234,125
Keep dividing by the next highest number until you cannot divide anymore.

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

1525311251555937759612,9653,8754,80514,82518,38324,02574,12591,915120,125459,575569,8732,297,8752,849,36514,246,82571,234,125
-1-5-25-31-125-155-593-775-961-2,965-3,875-4,805-14,825-18,383-24,025-74,125-91,915-120,125-459,575-569,873-2,297,875-2,849,365-14,246,825-71,234,125

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