Q: What are the factor combinations of the number 108,035,213?

 A:
Positive:   1 x 10803521311 x 982138313 x 8310401121 x 892853143 x 755491173 x 624481397 x 2721291573 x 686811903 x 567712249 x 480374367 x 247395161 x 20933
Negative: -1 x -108035213-11 x -9821383-13 x -8310401-121 x -892853-143 x -755491-173 x -624481-397 x -272129-1573 x -68681-1903 x -56771-2249 x -48037-4367 x -24739-5161 x -20933


How do I find the factor combinations of the number 108,035,213?

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 108,035,213, 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.

1 108,035,213
-1 -108,035,213

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 108,035,213.

Example:
1 x 108,035,213 = 108,035,213
and
-1 x -108,035,213 = 108,035,213
Notice both answers equal 108,035,213

With that explanation out of the way, let's continue. Next, we take the number 108,035,213 and divide it by 2:

108,035,213 ÷ 2 = 54,017,606.5

If the quotient is a whole number, then 2 and 54,017,606.5 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:

1 108,035,213
-1 -108,035,213

Now, we try dividing 108,035,213 by 3:

108,035,213 ÷ 3 = 36,011,737.6667

If the quotient is a whole number, then 3 and 36,011,737.6667 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:

1 108,035,213
-1 -108,035,213

Let's try dividing by 4:

108,035,213 ÷ 4 = 27,008,803.25

If the quotient is a whole number, then 4 and 27,008,803.25 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:

1 108,035,213
-1 108,035,213
Keep dividing by the next highest number until you cannot divide anymore.

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

111131211431733971,5731,9032,2494,3675,16120,93324,73948,03756,77168,681272,129624,481755,491892,8538,310,4019,821,383108,035,213
-1-11-13-121-143-173-397-1,573-1,903-2,249-4,367-5,161-20,933-24,739-48,037-56,771-68,681-272,129-624,481-755,491-892,853-8,310,401-9,821,383-108,035,213

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