Q: What are the factor combinations of the number 104,021,225?

 A:
Positive:   1 x 1040212255 x 208042457 x 1486017511 x 945647525 x 416084935 x 297203555 x 189129577 x 1350925175 x 594407275 x 378259385 x 2701851925 x 54037
Negative: -1 x -104021225-5 x -20804245-7 x -14860175-11 x -9456475-25 x -4160849-35 x -2972035-55 x -1891295-77 x -1350925-175 x -594407-275 x -378259-385 x -270185-1925 x -54037


How do I find the factor combinations of the number 104,021,225?

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 104,021,225, 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.

1 104,021,225
-1 -104,021,225

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 104,021,225.

Example:
1 x 104,021,225 = 104,021,225
and
-1 x -104,021,225 = 104,021,225
Notice both answers equal 104,021,225

With that explanation out of the way, let's continue. Next, we take the number 104,021,225 and divide it by 2:

104,021,225 ÷ 2 = 52,010,612.5

If the quotient is a whole number, then 2 and 52,010,612.5 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:

1 104,021,225
-1 -104,021,225

Now, we try dividing 104,021,225 by 3:

104,021,225 ÷ 3 = 34,673,741.6667

If the quotient is a whole number, then 3 and 34,673,741.6667 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:

1 104,021,225
-1 -104,021,225

Let's try dividing by 4:

104,021,225 ÷ 4 = 26,005,306.25

If the quotient is a whole number, then 4 and 26,005,306.25 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:

1 104,021,225
-1 104,021,225
Keep dividing by the next highest number until you cannot divide anymore.

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

15711253555771752753851,92554,037270,185378,259594,4071,350,9251,891,2952,972,0354,160,8499,456,47514,860,17520,804,245104,021,225
-1-5-7-11-25-35-55-77-175-275-385-1,925-54,037-270,185-378,259-594,407-1,350,925-1,891,295-2,972,035-4,160,849-9,456,475-14,860,175-20,804,245-104,021,225

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