Q: What are the factor combinations of the number 109,466,123?

 A:
Positive:   1 x 10946612313 x 8420471101 x 1083823263 x 416221317 x 3453191313 x 833713419 x 320174121 x 26563
Negative: -1 x -109466123-13 x -8420471-101 x -1083823-263 x -416221-317 x -345319-1313 x -83371-3419 x -32017-4121 x -26563


How do I find the factor combinations of the number 109,466,123?

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 109,466,123, 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.

1 109,466,123
-1 -109,466,123

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 109,466,123.

Example:
1 x 109,466,123 = 109,466,123
and
-1 x -109,466,123 = 109,466,123
Notice both answers equal 109,466,123

With that explanation out of the way, let's continue. Next, we take the number 109,466,123 and divide it by 2:

109,466,123 ÷ 2 = 54,733,061.5

If the quotient is a whole number, then 2 and 54,733,061.5 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:

1 109,466,123
-1 -109,466,123

Now, we try dividing 109,466,123 by 3:

109,466,123 ÷ 3 = 36,488,707.6667

If the quotient is a whole number, then 3 and 36,488,707.6667 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:

1 109,466,123
-1 -109,466,123

Let's try dividing by 4:

109,466,123 ÷ 4 = 27,366,530.75

If the quotient is a whole number, then 4 and 27,366,530.75 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:

1 109,466,123
-1 109,466,123
Keep dividing by the next highest number until you cannot divide anymore.

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

1131012633171,3133,4194,12126,56332,01783,371345,319416,2211,083,8238,420,471109,466,123
-1-13-101-263-317-1,313-3,419-4,121-26,563-32,017-83,371-345,319-416,221-1,083,823-8,420,471-109,466,123

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