Q: What are the factor combinations of the number 21,609,601?

 A:
Positive:   1 x 2160960113 x 166227717 x 1271153221 x 97781277 x 78013353 x 612173601 x 60014589 x 4709
Negative: -1 x -21609601-13 x -1662277-17 x -1271153-221 x -97781-277 x -78013-353 x -61217-3601 x -6001-4589 x -4709


How do I find the factor combinations of the number 21,609,601?

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 21,609,601, 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 21,609,601
-1 -21,609,601

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 21,609,601.

Example:
1 x 21,609,601 = 21,609,601
and
-1 x -21,609,601 = 21,609,601
Notice both answers equal 21,609,601

With that explanation out of the way, let's continue. Next, we take the number 21,609,601 and divide it by 2:

21,609,601 ÷ 2 = 10,804,800.5

If the quotient is a whole number, then 2 and 10,804,800.5 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 21,609,601
-1 -21,609,601

Now, we try dividing 21,609,601 by 3:

21,609,601 ÷ 3 = 7,203,200.3333

If the quotient is a whole number, then 3 and 7,203,200.3333 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 21,609,601
-1 -21,609,601

Let's try dividing by 4:

21,609,601 ÷ 4 = 5,402,400.25

If the quotient is a whole number, then 4 and 5,402,400.25 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 21,609,601
-1 21,609,601
Keep dividing by the next highest number until you cannot divide anymore.

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

113172212773533,6014,5894,7096,00161,21778,01397,7811,271,1531,662,27721,609,601
-1-13-17-221-277-353-3,601-4,589-4,709-6,001-61,217-78,013-97,781-1,271,153-1,662,277-21,609,601

More Examples

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