Q: What are the factor combinations of the number 21,227,731?

 A:
Positive:   1 x 212277317 x 303253319 x 111724949 x 433219133 x 159607151 x 140581931 x 228011057 x 200832869 x 7399
Negative: -1 x -21227731-7 x -3032533-19 x -1117249-49 x -433219-133 x -159607-151 x -140581-931 x -22801-1057 x -20083-2869 x -7399


How do I find the factor combinations of the number 21,227,731?

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 21,227,731, 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 21,227,731
-1 -21,227,731

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 21,227,731.

Example:
1 x 21,227,731 = 21,227,731
and
-1 x -21,227,731 = 21,227,731
Notice both answers equal 21,227,731

With that explanation out of the way, let's continue. Next, we take the number 21,227,731 and divide it by 2:

21,227,731 ÷ 2 = 10,613,865.5

If the quotient is a whole number, then 2 and 10,613,865.5 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 21,227,731
-1 -21,227,731

Now, we try dividing 21,227,731 by 3:

21,227,731 ÷ 3 = 7,075,910.3333

If the quotient is a whole number, then 3 and 7,075,910.3333 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 21,227,731
-1 -21,227,731

Let's try dividing by 4:

21,227,731 ÷ 4 = 5,306,932.75

If the quotient is a whole number, then 4 and 5,306,932.75 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 21,227,731
-1 21,227,731
Keep dividing by the next highest number until you cannot divide anymore.

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

1719491331519311,0572,8697,39920,08322,801140,581159,607433,2191,117,2493,032,53321,227,731
-1-7-19-49-133-151-931-1,057-2,869-7,399-20,083-22,801-140,581-159,607-433,219-1,117,249-3,032,533-21,227,731

More Examples

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