Q: What are the factor combinations of the number 24,300,311?

 A:
Positive:   1 x 243003117 x 347147331 x 783881113 x 215047217 x 111983791 x 30721991 x 245213503 x 6937
Negative: -1 x -24300311-7 x -3471473-31 x -783881-113 x -215047-217 x -111983-791 x -30721-991 x -24521-3503 x -6937


How do I find the factor combinations of the number 24,300,311?

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 24,300,311, 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 24,300,311
-1 -24,300,311

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 24,300,311.

Example:
1 x 24,300,311 = 24,300,311
and
-1 x -24,300,311 = 24,300,311
Notice both answers equal 24,300,311

With that explanation out of the way, let's continue. Next, we take the number 24,300,311 and divide it by 2:

24,300,311 ÷ 2 = 12,150,155.5

If the quotient is a whole number, then 2 and 12,150,155.5 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 24,300,311
-1 -24,300,311

Now, we try dividing 24,300,311 by 3:

24,300,311 ÷ 3 = 8,100,103.6667

If the quotient is a whole number, then 3 and 8,100,103.6667 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 24,300,311
-1 -24,300,311

Let's try dividing by 4:

24,300,311 ÷ 4 = 6,075,077.75

If the quotient is a whole number, then 4 and 6,075,077.75 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 24,300,311
-1 24,300,311
Keep dividing by the next highest number until you cannot divide anymore.

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

17311132177919913,5036,93724,52130,721111,983215,047783,8813,471,47324,300,311
-1-7-31-113-217-791-991-3,503-6,937-24,521-30,721-111,983-215,047-783,881-3,471,473-24,300,311

More Examples

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