Q: What are the factor combinations of the number 40,212,227?

 A:
Positive:   1 x 4021222711 x 365565719 x 2116433181 x 222167209 x 1924031063 x 378291991 x 201973439 x 11693
Negative: -1 x -40212227-11 x -3655657-19 x -2116433-181 x -222167-209 x -192403-1063 x -37829-1991 x -20197-3439 x -11693


How do I find the factor combinations of the number 40,212,227?

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 40,212,227, 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 40,212,227
-1 -40,212,227

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 40,212,227.

Example:
1 x 40,212,227 = 40,212,227
and
-1 x -40,212,227 = 40,212,227
Notice both answers equal 40,212,227

With that explanation out of the way, let's continue. Next, we take the number 40,212,227 and divide it by 2:

40,212,227 ÷ 2 = 20,106,113.5

If the quotient is a whole number, then 2 and 20,106,113.5 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 40,212,227
-1 -40,212,227

Now, we try dividing 40,212,227 by 3:

40,212,227 ÷ 3 = 13,404,075.6667

If the quotient is a whole number, then 3 and 13,404,075.6667 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 40,212,227
-1 -40,212,227

Let's try dividing by 4:

40,212,227 ÷ 4 = 10,053,056.75

If the quotient is a whole number, then 4 and 10,053,056.75 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 40,212,227
-1 40,212,227
Keep dividing by the next highest number until you cannot divide anymore.

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

111191812091,0631,9913,43911,69320,19737,829192,403222,1672,116,4333,655,65740,212,227
-1-11-19-181-209-1,063-1,991-3,439-11,693-20,197-37,829-192,403-222,167-2,116,433-3,655,657-40,212,227

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