Q: What are the factor combinations of the number 21,034,121?

 A:
Positive:   1 x 2103412119 x 110705923 x 914527127 x 165623379 x 55499437 x 481332413 x 87172921 x 7201
Negative: -1 x -21034121-19 x -1107059-23 x -914527-127 x -165623-379 x -55499-437 x -48133-2413 x -8717-2921 x -7201


How do I find the factor combinations of the number 21,034,121?

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 21,034,121, 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 21,034,121
-1 -21,034,121

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 21,034,121.

Example:
1 x 21,034,121 = 21,034,121
and
-1 x -21,034,121 = 21,034,121
Notice both answers equal 21,034,121

With that explanation out of the way, let's continue. Next, we take the number 21,034,121 and divide it by 2:

21,034,121 ÷ 2 = 10,517,060.5

If the quotient is a whole number, then 2 and 10,517,060.5 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 21,034,121
-1 -21,034,121

Now, we try dividing 21,034,121 by 3:

21,034,121 ÷ 3 = 7,011,373.6667

If the quotient is a whole number, then 3 and 7,011,373.6667 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 21,034,121
-1 -21,034,121

Let's try dividing by 4:

21,034,121 ÷ 4 = 5,258,530.25

If the quotient is a whole number, then 4 and 5,258,530.25 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 21,034,121
-1 21,034,121
Keep dividing by the next highest number until you cannot divide anymore.

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

119231273794372,4132,9217,2018,71748,13355,499165,623914,5271,107,05921,034,121
-1-19-23-127-379-437-2,413-2,921-7,201-8,717-48,133-55,499-165,623-914,527-1,107,059-21,034,121

More Examples

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