Q: What are the factor combinations of the number 29,688,749?

 A:
Positive:   1 x 2968874917 x 1746397
Negative: -1 x -29688749-17 x -1746397


How do I find the factor combinations of the number 29,688,749?

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 29,688,749, 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 29,688,749
-1 -29,688,749

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 29,688,749.

Example:
1 x 29,688,749 = 29,688,749
and
-1 x -29,688,749 = 29,688,749
Notice both answers equal 29,688,749

With that explanation out of the way, let's continue. Next, we take the number 29,688,749 and divide it by 2:

29,688,749 ÷ 2 = 14,844,374.5

If the quotient is a whole number, then 2 and 14,844,374.5 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 29,688,749
-1 -29,688,749

Now, we try dividing 29,688,749 by 3:

29,688,749 ÷ 3 = 9,896,249.6667

If the quotient is a whole number, then 3 and 9,896,249.6667 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 29,688,749
-1 -29,688,749

Let's try dividing by 4:

29,688,749 ÷ 4 = 7,422,187.25

If the quotient is a whole number, then 4 and 7,422,187.25 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 29,688,749
-1 29,688,749
Keep dividing by the next highest number until you cannot divide anymore.

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

1171,746,39729,688,749
-1-17-1,746,397-29,688,749

More Examples

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