Q: What are the factor combinations of the number 43,689,125?

 A:
Positive:   1 x 436891255 x 873782525 x 174756583 x 526375125 x 349513415 x 1052752075 x 210554211 x 10375
Negative: -1 x -43689125-5 x -8737825-25 x -1747565-83 x -526375-125 x -349513-415 x -105275-2075 x -21055-4211 x -10375


How do I find the factor combinations of the number 43,689,125?

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 43,689,125, 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 43,689,125
-1 -43,689,125

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 43,689,125.

Example:
1 x 43,689,125 = 43,689,125
and
-1 x -43,689,125 = 43,689,125
Notice both answers equal 43,689,125

With that explanation out of the way, let's continue. Next, we take the number 43,689,125 and divide it by 2:

43,689,125 ÷ 2 = 21,844,562.5

If the quotient is a whole number, then 2 and 21,844,562.5 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 43,689,125
-1 -43,689,125

Now, we try dividing 43,689,125 by 3:

43,689,125 ÷ 3 = 14,563,041.6667

If the quotient is a whole number, then 3 and 14,563,041.6667 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 43,689,125
-1 -43,689,125

Let's try dividing by 4:

43,689,125 ÷ 4 = 10,922,281.25

If the quotient is a whole number, then 4 and 10,922,281.25 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 43,689,125
-1 43,689,125
Keep dividing by the next highest number until you cannot divide anymore.

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

1525831254152,0754,21110,37521,055105,275349,513526,3751,747,5658,737,82543,689,125
-1-5-25-83-125-415-2,075-4,211-10,375-21,055-105,275-349,513-526,375-1,747,565-8,737,825-43,689,125

More Examples

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