Q: What are the factor combinations of the number 29,026,129?

 A:
Positive:   1 x 2902612911 x 263873919 x 152769129 x 1000901209 x 138881319 x 90991551 x 526794789 x 6061
Negative: -1 x -29026129-11 x -2638739-19 x -1527691-29 x -1000901-209 x -138881-319 x -90991-551 x -52679-4789 x -6061


How do I find the factor combinations of the number 29,026,129?

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 29,026,129, 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 29,026,129
-1 -29,026,129

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 29,026,129.

Example:
1 x 29,026,129 = 29,026,129
and
-1 x -29,026,129 = 29,026,129
Notice both answers equal 29,026,129

With that explanation out of the way, let's continue. Next, we take the number 29,026,129 and divide it by 2:

29,026,129 ÷ 2 = 14,513,064.5

If the quotient is a whole number, then 2 and 14,513,064.5 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 29,026,129
-1 -29,026,129

Now, we try dividing 29,026,129 by 3:

29,026,129 ÷ 3 = 9,675,376.3333

If the quotient is a whole number, then 3 and 9,675,376.3333 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 29,026,129
-1 -29,026,129

Let's try dividing by 4:

29,026,129 ÷ 4 = 7,256,532.25

If the quotient is a whole number, then 4 and 7,256,532.25 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 29,026,129
-1 29,026,129
Keep dividing by the next highest number until you cannot divide anymore.

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

11119292093195514,7896,06152,67990,991138,8811,000,9011,527,6912,638,73929,026,129
-1-11-19-29-209-319-551-4,789-6,061-52,679-90,991-138,881-1,000,901-1,527,691-2,638,739-29,026,129

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