Q: What are the factor combinations of the number 105,055,435?

 A:
Positive:   1 x 1050554355 x 2101108731 x 3388885155 x 677777571 x 1839851187 x 885052855 x 367975935 x 17701
Negative: -1 x -105055435-5 x -21011087-31 x -3388885-155 x -677777-571 x -183985-1187 x -88505-2855 x -36797-5935 x -17701


How do I find the factor combinations of the number 105,055,435?

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 105,055,435, 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.

1 105,055,435
-1 -105,055,435

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 105,055,435.

Example:
1 x 105,055,435 = 105,055,435
and
-1 x -105,055,435 = 105,055,435
Notice both answers equal 105,055,435

With that explanation out of the way, let's continue. Next, we take the number 105,055,435 and divide it by 2:

105,055,435 ÷ 2 = 52,527,717.5

If the quotient is a whole number, then 2 and 52,527,717.5 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:

1 105,055,435
-1 -105,055,435

Now, we try dividing 105,055,435 by 3:

105,055,435 ÷ 3 = 35,018,478.3333

If the quotient is a whole number, then 3 and 35,018,478.3333 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:

1 105,055,435
-1 -105,055,435

Let's try dividing by 4:

105,055,435 ÷ 4 = 26,263,858.75

If the quotient is a whole number, then 4 and 26,263,858.75 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:

1 105,055,435
-1 105,055,435
Keep dividing by the next highest number until you cannot divide anymore.

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

15311555711,1872,8555,93517,70136,79788,505183,985677,7773,388,88521,011,087105,055,435
-1-5-31-155-571-1,187-2,855-5,935-17,701-36,797-88,505-183,985-677,777-3,388,885-21,011,087-105,055,435

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