Q: What are the factor combinations of the number 103,240,123?

 A:
Positive:   1 x 1032401237 x 1474858923 x 448870179 x 1306837161 x 641243553 x 1866911817 x 568198117 x 12719
Negative: -1 x -103240123-7 x -14748589-23 x -4488701-79 x -1306837-161 x -641243-553 x -186691-1817 x -56819-8117 x -12719


How do I find the factor combinations of the number 103,240,123?

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 103,240,123, 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.

1 103,240,123
-1 -103,240,123

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 103,240,123.

Example:
1 x 103,240,123 = 103,240,123
and
-1 x -103,240,123 = 103,240,123
Notice both answers equal 103,240,123

With that explanation out of the way, let's continue. Next, we take the number 103,240,123 and divide it by 2:

103,240,123 ÷ 2 = 51,620,061.5

If the quotient is a whole number, then 2 and 51,620,061.5 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:

1 103,240,123
-1 -103,240,123

Now, we try dividing 103,240,123 by 3:

103,240,123 ÷ 3 = 34,413,374.3333

If the quotient is a whole number, then 3 and 34,413,374.3333 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:

1 103,240,123
-1 -103,240,123

Let's try dividing by 4:

103,240,123 ÷ 4 = 25,810,030.75

If the quotient is a whole number, then 4 and 25,810,030.75 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:

1 103,240,123
-1 103,240,123
Keep dividing by the next highest number until you cannot divide anymore.

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

1723791615531,8178,11712,71956,819186,691641,2431,306,8374,488,70114,748,589103,240,123
-1-7-23-79-161-553-1,817-8,117-12,719-56,819-186,691-641,243-1,306,837-4,488,701-14,748,589-103,240,123

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