Q: What are the factor combinations of the number 29,869?

 A:
Positive:   1 x 298697 x 426717 x 1757119 x 251
Negative: -1 x -29869-7 x -4267-17 x -1757-119 x -251


How do I find the factor combinations of the number 29,869?

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 29,869, 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 29,869
-1 -29,869

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 29,869.

Example:
1 x 29,869 = 29,869
and
-1 x -29,869 = 29,869
Notice both answers equal 29,869

With that explanation out of the way, let's continue. Next, we take the number 29,869 and divide it by 2:

29,869 ÷ 2 = 14,934.5

If the quotient is a whole number, then 2 and 14,934.5 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 29,869
-1 -29,869

Now, we try dividing 29,869 by 3:

29,869 ÷ 3 = 9,956.3333

If the quotient is a whole number, then 3 and 9,956.3333 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 29,869
-1 -29,869

Let's try dividing by 4:

29,869 ÷ 4 = 7,467.25

If the quotient is a whole number, then 4 and 7,467.25 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 29,869
-1 29,869
Keep dividing by the next highest number until you cannot divide anymore.

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

17171192511,7574,26729,869
-1-7-17-119-251-1,757-4,267-29,869

More Examples

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