Q: What are the factor combinations of the number 40,295,609?

 A:
Positive:   1 x 4029560923 x 175198367 x 60142779 x 510071331 x 1217391541 x 261491817 x 221775293 x 7613
Negative: -1 x -40295609-23 x -1751983-67 x -601427-79 x -510071-331 x -121739-1541 x -26149-1817 x -22177-5293 x -7613


How do I find the factor combinations of the number 40,295,609?

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 40,295,609, 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 40,295,609
-1 -40,295,609

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 40,295,609.

Example:
1 x 40,295,609 = 40,295,609
and
-1 x -40,295,609 = 40,295,609
Notice both answers equal 40,295,609

With that explanation out of the way, let's continue. Next, we take the number 40,295,609 and divide it by 2:

40,295,609 ÷ 2 = 20,147,804.5

If the quotient is a whole number, then 2 and 20,147,804.5 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 40,295,609
-1 -40,295,609

Now, we try dividing 40,295,609 by 3:

40,295,609 ÷ 3 = 13,431,869.6667

If the quotient is a whole number, then 3 and 13,431,869.6667 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 40,295,609
-1 -40,295,609

Let's try dividing by 4:

40,295,609 ÷ 4 = 10,073,902.25

If the quotient is a whole number, then 4 and 10,073,902.25 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 40,295,609
-1 40,295,609
Keep dividing by the next highest number until you cannot divide anymore.

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

12367793311,5411,8175,2937,61322,17726,149121,739510,071601,4271,751,98340,295,609
-1-23-67-79-331-1,541-1,817-5,293-7,613-22,177-26,149-121,739-510,071-601,427-1,751,983-40,295,609

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