Q: What are the factor combinations of the number 24,312,029?

 A:
Positive:   1 x 243120297 x 347314731 x 784259199 x 122171217 x 112037563 x 431831393 x 174533941 x 6169
Negative: -1 x -24312029-7 x -3473147-31 x -784259-199 x -122171-217 x -112037-563 x -43183-1393 x -17453-3941 x -6169


How do I find the factor combinations of the number 24,312,029?

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 24,312,029, 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 24,312,029
-1 -24,312,029

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 24,312,029.

Example:
1 x 24,312,029 = 24,312,029
and
-1 x -24,312,029 = 24,312,029
Notice both answers equal 24,312,029

With that explanation out of the way, let's continue. Next, we take the number 24,312,029 and divide it by 2:

24,312,029 ÷ 2 = 12,156,014.5

If the quotient is a whole number, then 2 and 12,156,014.5 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 24,312,029
-1 -24,312,029

Now, we try dividing 24,312,029 by 3:

24,312,029 ÷ 3 = 8,104,009.6667

If the quotient is a whole number, then 3 and 8,104,009.6667 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 24,312,029
-1 -24,312,029

Let's try dividing by 4:

24,312,029 ÷ 4 = 6,078,007.25

If the quotient is a whole number, then 4 and 6,078,007.25 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 24,312,029
-1 24,312,029
Keep dividing by the next highest number until you cannot divide anymore.

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

17311992175631,3933,9416,16917,45343,183112,037122,171784,2593,473,14724,312,029
-1-7-31-199-217-563-1,393-3,941-6,169-17,453-43,183-112,037-122,171-784,259-3,473,147-24,312,029

More Examples

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