Q: What are the factor combinations of the number 21,200,123?

 A:
Positive:   1 x 212001237 x 302858961 x 347543131 x 161833379 x 55937427 x 49649917 x 231192653 x 7991
Negative: -1 x -21200123-7 x -3028589-61 x -347543-131 x -161833-379 x -55937-427 x -49649-917 x -23119-2653 x -7991


How do I find the factor combinations of the number 21,200,123?

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 21,200,123, 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 21,200,123
-1 -21,200,123

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 21,200,123.

Example:
1 x 21,200,123 = 21,200,123
and
-1 x -21,200,123 = 21,200,123
Notice both answers equal 21,200,123

With that explanation out of the way, let's continue. Next, we take the number 21,200,123 and divide it by 2:

21,200,123 ÷ 2 = 10,600,061.5

If the quotient is a whole number, then 2 and 10,600,061.5 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 21,200,123
-1 -21,200,123

Now, we try dividing 21,200,123 by 3:

21,200,123 ÷ 3 = 7,066,707.6667

If the quotient is a whole number, then 3 and 7,066,707.6667 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 21,200,123
-1 -21,200,123

Let's try dividing by 4:

21,200,123 ÷ 4 = 5,300,030.75

If the quotient is a whole number, then 4 and 5,300,030.75 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 21,200,123
-1 21,200,123
Keep dividing by the next highest number until you cannot divide anymore.

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

17611313794279172,6537,99123,11949,64955,937161,833347,5433,028,58921,200,123
-1-7-61-131-379-427-917-2,653-7,991-23,119-49,649-55,937-161,833-347,543-3,028,589-21,200,123

More Examples

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