Q: What are the factor combinations of the number 102,025,517?

 A:
Positive:   1 x 10202551711 x 927504717 x 6001501103 x 990539187 x 5455911133 x 900491751 x 582675297 x 19261
Negative: -1 x -102025517-11 x -9275047-17 x -6001501-103 x -990539-187 x -545591-1133 x -90049-1751 x -58267-5297 x -19261


How do I find the factor combinations of the number 102,025,517?

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 102,025,517, 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.

1 102,025,517
-1 -102,025,517

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 102,025,517.

Example:
1 x 102,025,517 = 102,025,517
and
-1 x -102,025,517 = 102,025,517
Notice both answers equal 102,025,517

With that explanation out of the way, let's continue. Next, we take the number 102,025,517 and divide it by 2:

102,025,517 ÷ 2 = 51,012,758.5

If the quotient is a whole number, then 2 and 51,012,758.5 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:

1 102,025,517
-1 -102,025,517

Now, we try dividing 102,025,517 by 3:

102,025,517 ÷ 3 = 34,008,505.6667

If the quotient is a whole number, then 3 and 34,008,505.6667 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:

1 102,025,517
-1 -102,025,517

Let's try dividing by 4:

102,025,517 ÷ 4 = 25,506,379.25

If the quotient is a whole number, then 4 and 25,506,379.25 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:

1 102,025,517
-1 102,025,517
Keep dividing by the next highest number until you cannot divide anymore.

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

111171031871,1331,7515,29719,26158,26790,049545,591990,5396,001,5019,275,047102,025,517
-1-11-17-103-187-1,133-1,751-5,297-19,261-58,267-90,049-545,591-990,539-6,001,501-9,275,047-102,025,517

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