Q: What are the factor combinations of the number 43,660,309?

 A:
Positive:   1 x 436603097 x 623718711 x 396911919 x 229791177 x 567017121 x 360829133 x 328273209 x 208901847 x 515471463 x 298432299 x 189912713 x 16093
Negative: -1 x -43660309-7 x -6237187-11 x -3969119-19 x -2297911-77 x -567017-121 x -360829-133 x -328273-209 x -208901-847 x -51547-1463 x -29843-2299 x -18991-2713 x -16093


How do I find the factor combinations of the number 43,660,309?

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 43,660,309, 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 43,660,309
-1 -43,660,309

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 43,660,309.

Example:
1 x 43,660,309 = 43,660,309
and
-1 x -43,660,309 = 43,660,309
Notice both answers equal 43,660,309

With that explanation out of the way, let's continue. Next, we take the number 43,660,309 and divide it by 2:

43,660,309 ÷ 2 = 21,830,154.5

If the quotient is a whole number, then 2 and 21,830,154.5 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 43,660,309
-1 -43,660,309

Now, we try dividing 43,660,309 by 3:

43,660,309 ÷ 3 = 14,553,436.3333

If the quotient is a whole number, then 3 and 14,553,436.3333 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 43,660,309
-1 -43,660,309

Let's try dividing by 4:

43,660,309 ÷ 4 = 10,915,077.25

If the quotient is a whole number, then 4 and 10,915,077.25 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 43,660,309
-1 43,660,309
Keep dividing by the next highest number until you cannot divide anymore.

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

171119771211332098471,4632,2992,71316,09318,99129,84351,547208,901328,273360,829567,0172,297,9113,969,1196,237,18743,660,309
-1-7-11-19-77-121-133-209-847-1,463-2,299-2,713-16,093-18,991-29,843-51,547-208,901-328,273-360,829-567,017-2,297,911-3,969,119-6,237,187-43,660,309

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