Q: What are the factor combinations of the number 47,531,405?

 A:
Positive:   1 x 475314055 x 950628117 x 279596585 x 559193461 x 1031051213 x 391852305 x 206216065 x 7837
Negative: -1 x -47531405-5 x -9506281-17 x -2795965-85 x -559193-461 x -103105-1213 x -39185-2305 x -20621-6065 x -7837


How do I find the factor combinations of the number 47,531,405?

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 47,531,405, 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 47,531,405
-1 -47,531,405

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 47,531,405.

Example:
1 x 47,531,405 = 47,531,405
and
-1 x -47,531,405 = 47,531,405
Notice both answers equal 47,531,405

With that explanation out of the way, let's continue. Next, we take the number 47,531,405 and divide it by 2:

47,531,405 ÷ 2 = 23,765,702.5

If the quotient is a whole number, then 2 and 23,765,702.5 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 47,531,405
-1 -47,531,405

Now, we try dividing 47,531,405 by 3:

47,531,405 ÷ 3 = 15,843,801.6667

If the quotient is a whole number, then 3 and 15,843,801.6667 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 47,531,405
-1 -47,531,405

Let's try dividing by 4:

47,531,405 ÷ 4 = 11,882,851.25

If the quotient is a whole number, then 4 and 11,882,851.25 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 47,531,405
-1 47,531,405
Keep dividing by the next highest number until you cannot divide anymore.

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

1517854611,2132,3056,0657,83720,62139,185103,105559,1932,795,9659,506,28147,531,405
-1-5-17-85-461-1,213-2,305-6,065-7,837-20,621-39,185-103,105-559,193-2,795,965-9,506,281-47,531,405

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