Q: What are the factor combinations of the number 40,135,205?

 A:
Positive:   1 x 401352055 x 802704111 x 364865555 x 72973197 x 413765485 x 827531067 x 376155335 x 7523
Negative: -1 x -40135205-5 x -8027041-11 x -3648655-55 x -729731-97 x -413765-485 x -82753-1067 x -37615-5335 x -7523


How do I find the factor combinations of the number 40,135,205?

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 40,135,205, 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 40,135,205
-1 -40,135,205

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 40,135,205.

Example:
1 x 40,135,205 = 40,135,205
and
-1 x -40,135,205 = 40,135,205
Notice both answers equal 40,135,205

With that explanation out of the way, let's continue. Next, we take the number 40,135,205 and divide it by 2:

40,135,205 ÷ 2 = 20,067,602.5

If the quotient is a whole number, then 2 and 20,067,602.5 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 40,135,205
-1 -40,135,205

Now, we try dividing 40,135,205 by 3:

40,135,205 ÷ 3 = 13,378,401.6667

If the quotient is a whole number, then 3 and 13,378,401.6667 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 40,135,205
-1 -40,135,205

Let's try dividing by 4:

40,135,205 ÷ 4 = 10,033,801.25

If the quotient is a whole number, then 4 and 10,033,801.25 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 40,135,205
-1 40,135,205
Keep dividing by the next highest number until you cannot divide anymore.

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

151155974851,0675,3357,52337,61582,753413,765729,7313,648,6558,027,04140,135,205
-1-5-11-55-97-485-1,067-5,335-7,523-37,615-82,753-413,765-729,731-3,648,655-8,027,041-40,135,205

More Examples

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