Q: What are the factor combinations of the number 21,401,237?

 A:
Positive:   1 x 2140123711 x 194556713 x 1646249103 x 207779143 x 1496591133 x 188891339 x 159831453 x 14729
Negative: -1 x -21401237-11 x -1945567-13 x -1646249-103 x -207779-143 x -149659-1133 x -18889-1339 x -15983-1453 x -14729


How do I find the factor combinations of the number 21,401,237?

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 21,401,237, 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 21,401,237
-1 -21,401,237

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 21,401,237.

Example:
1 x 21,401,237 = 21,401,237
and
-1 x -21,401,237 = 21,401,237
Notice both answers equal 21,401,237

With that explanation out of the way, let's continue. Next, we take the number 21,401,237 and divide it by 2:

21,401,237 ÷ 2 = 10,700,618.5

If the quotient is a whole number, then 2 and 10,700,618.5 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 21,401,237
-1 -21,401,237

Now, we try dividing 21,401,237 by 3:

21,401,237 ÷ 3 = 7,133,745.6667

If the quotient is a whole number, then 3 and 7,133,745.6667 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 21,401,237
-1 -21,401,237

Let's try dividing by 4:

21,401,237 ÷ 4 = 5,350,309.25

If the quotient is a whole number, then 4 and 5,350,309.25 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 21,401,237
-1 21,401,237
Keep dividing by the next highest number until you cannot divide anymore.

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

111131031431,1331,3391,45314,72915,98318,889149,659207,7791,646,2491,945,56721,401,237
-1-11-13-103-143-1,133-1,339-1,453-14,729-15,983-18,889-149,659-207,779-1,646,249-1,945,567-21,401,237

More Examples

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