Q: What are the factor combinations of the number 21,000,133?

 A:
Positive:   1 x 210001337 x 300001911 x 190910377 x 272729223 x 941711223 x 171711561 x 134532453 x 8561
Negative: -1 x -21000133-7 x -3000019-11 x -1909103-77 x -272729-223 x -94171-1223 x -17171-1561 x -13453-2453 x -8561


How do I find the factor combinations of the number 21,000,133?

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 21,000,133, 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 21,000,133
-1 -21,000,133

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 21,000,133.

Example:
1 x 21,000,133 = 21,000,133
and
-1 x -21,000,133 = 21,000,133
Notice both answers equal 21,000,133

With that explanation out of the way, let's continue. Next, we take the number 21,000,133 and divide it by 2:

21,000,133 ÷ 2 = 10,500,066.5

If the quotient is a whole number, then 2 and 10,500,066.5 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 21,000,133
-1 -21,000,133

Now, we try dividing 21,000,133 by 3:

21,000,133 ÷ 3 = 7,000,044.3333

If the quotient is a whole number, then 3 and 7,000,044.3333 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 21,000,133
-1 -21,000,133

Let's try dividing by 4:

21,000,133 ÷ 4 = 5,250,033.25

If the quotient is a whole number, then 4 and 5,250,033.25 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 21,000,133
-1 21,000,133
Keep dividing by the next highest number until you cannot divide anymore.

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

1711772231,2231,5612,4538,56113,45317,17194,171272,7291,909,1033,000,01921,000,133
-1-7-11-77-223-1,223-1,561-2,453-8,561-13,453-17,171-94,171-272,729-1,909,103-3,000,019-21,000,133

More Examples

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