Q: What are the factor combinations of the number 109,077,251?

 A:
Positive:   1 x 10907725131 x 3518621383 x 2847979187 x 11873
Negative: -1 x -109077251-31 x -3518621-383 x -284797-9187 x -11873


How do I find the factor combinations of the number 109,077,251?

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 109,077,251, 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.

1 109,077,251
-1 -109,077,251

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 109,077,251.

Example:
1 x 109,077,251 = 109,077,251
and
-1 x -109,077,251 = 109,077,251
Notice both answers equal 109,077,251

With that explanation out of the way, let's continue. Next, we take the number 109,077,251 and divide it by 2:

109,077,251 ÷ 2 = 54,538,625.5

If the quotient is a whole number, then 2 and 54,538,625.5 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:

1 109,077,251
-1 -109,077,251

Now, we try dividing 109,077,251 by 3:

109,077,251 ÷ 3 = 36,359,083.6667

If the quotient is a whole number, then 3 and 36,359,083.6667 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:

1 109,077,251
-1 -109,077,251

Let's try dividing by 4:

109,077,251 ÷ 4 = 27,269,312.75

If the quotient is a whole number, then 4 and 27,269,312.75 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:

1 109,077,251
-1 109,077,251
Keep dividing by the next highest number until you cannot divide anymore.

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

1313839,18711,873284,7973,518,621109,077,251
-1-31-383-9,187-11,873-284,797-3,518,621-109,077,251

More Examples

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