Q: What are the factor combinations of the number 43,042,097?

 A:
Positive:   1 x 430420977 x 614887143 x 1000979151 x 285047301 x 142997947 x 454511057 x 407216493 x 6629
Negative: -1 x -43042097-7 x -6148871-43 x -1000979-151 x -285047-301 x -142997-947 x -45451-1057 x -40721-6493 x -6629


How do I find the factor combinations of the number 43,042,097?

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 43,042,097, 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 43,042,097
-1 -43,042,097

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 43,042,097.

Example:
1 x 43,042,097 = 43,042,097
and
-1 x -43,042,097 = 43,042,097
Notice both answers equal 43,042,097

With that explanation out of the way, let's continue. Next, we take the number 43,042,097 and divide it by 2:

43,042,097 ÷ 2 = 21,521,048.5

If the quotient is a whole number, then 2 and 21,521,048.5 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 43,042,097
-1 -43,042,097

Now, we try dividing 43,042,097 by 3:

43,042,097 ÷ 3 = 14,347,365.6667

If the quotient is a whole number, then 3 and 14,347,365.6667 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 43,042,097
-1 -43,042,097

Let's try dividing by 4:

43,042,097 ÷ 4 = 10,760,524.25

If the quotient is a whole number, then 4 and 10,760,524.25 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 43,042,097
-1 43,042,097
Keep dividing by the next highest number until you cannot divide anymore.

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

17431513019471,0576,4936,62940,72145,451142,997285,0471,000,9796,148,87143,042,097
-1-7-43-151-301-947-1,057-6,493-6,629-40,721-45,451-142,997-285,047-1,000,979-6,148,871-43,042,097

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