Q: What are the factor combinations of the number 21,102,035?

 A:
Positive:   1 x 211020355 x 422040743 x 49074561 x 345935215 x 98149305 x 691871609 x 131152623 x 8045
Negative: -1 x -21102035-5 x -4220407-43 x -490745-61 x -345935-215 x -98149-305 x -69187-1609 x -13115-2623 x -8045


How do I find the factor combinations of the number 21,102,035?

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 21,102,035, 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 21,102,035
-1 -21,102,035

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 21,102,035.

Example:
1 x 21,102,035 = 21,102,035
and
-1 x -21,102,035 = 21,102,035
Notice both answers equal 21,102,035

With that explanation out of the way, let's continue. Next, we take the number 21,102,035 and divide it by 2:

21,102,035 ÷ 2 = 10,551,017.5

If the quotient is a whole number, then 2 and 10,551,017.5 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 21,102,035
-1 -21,102,035

Now, we try dividing 21,102,035 by 3:

21,102,035 ÷ 3 = 7,034,011.6667

If the quotient is a whole number, then 3 and 7,034,011.6667 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 21,102,035
-1 -21,102,035

Let's try dividing by 4:

21,102,035 ÷ 4 = 5,275,508.75

If the quotient is a whole number, then 4 and 5,275,508.75 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 21,102,035
-1 21,102,035
Keep dividing by the next highest number until you cannot divide anymore.

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

1543612153051,6092,6238,04513,11569,18798,149345,935490,7454,220,40721,102,035
-1-5-43-61-215-305-1,609-2,623-8,045-13,115-69,187-98,149-345,935-490,745-4,220,407-21,102,035

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