Q: What are the factor combinations of the number 43,423,405?

 A:
Positive:   1 x 434234055 x 868468131 x 1400755155 x 280151433 x 100285647 x 671152165 x 200573235 x 13423
Negative: -1 x -43423405-5 x -8684681-31 x -1400755-155 x -280151-433 x -100285-647 x -67115-2165 x -20057-3235 x -13423


How do I find the factor combinations of the number 43,423,405?

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 43,423,405, 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 43,423,405
-1 -43,423,405

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 43,423,405.

Example:
1 x 43,423,405 = 43,423,405
and
-1 x -43,423,405 = 43,423,405
Notice both answers equal 43,423,405

With that explanation out of the way, let's continue. Next, we take the number 43,423,405 and divide it by 2:

43,423,405 ÷ 2 = 21,711,702.5

If the quotient is a whole number, then 2 and 21,711,702.5 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 43,423,405
-1 -43,423,405

Now, we try dividing 43,423,405 by 3:

43,423,405 ÷ 3 = 14,474,468.3333

If the quotient is a whole number, then 3 and 14,474,468.3333 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 43,423,405
-1 -43,423,405

Let's try dividing by 4:

43,423,405 ÷ 4 = 10,855,851.25

If the quotient is a whole number, then 4 and 10,855,851.25 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 43,423,405
-1 43,423,405
Keep dividing by the next highest number until you cannot divide anymore.

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

15311554336472,1653,23513,42320,05767,115100,285280,1511,400,7558,684,68143,423,405
-1-5-31-155-433-647-2,165-3,235-13,423-20,057-67,115-100,285-280,151-1,400,755-8,684,681-43,423,405

More Examples

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