Q: What are the factor combinations of the number 234,003,407?

 A:
Positive:   1 x 23400340711 x 2127303729 x 806908331 x 7548497319 x 733553341 x 686227899 x 2602939889 x 23663
Negative: -1 x -234003407-11 x -21273037-29 x -8069083-31 x -7548497-319 x -733553-341 x -686227-899 x -260293-9889 x -23663


How do I find the factor combinations of the number 234,003,407?

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 234,003,407, 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.

1 234,003,407
-1 -234,003,407

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 234,003,407.

Example:
1 x 234,003,407 = 234,003,407
and
-1 x -234,003,407 = 234,003,407
Notice both answers equal 234,003,407

With that explanation out of the way, let's continue. Next, we take the number 234,003,407 and divide it by 2:

234,003,407 ÷ 2 = 117,001,703.5

If the quotient is a whole number, then 2 and 117,001,703.5 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:

1 234,003,407
-1 -234,003,407

Now, we try dividing 234,003,407 by 3:

234,003,407 ÷ 3 = 78,001,135.6667

If the quotient is a whole number, then 3 and 78,001,135.6667 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:

1 234,003,407
-1 -234,003,407

Let's try dividing by 4:

234,003,407 ÷ 4 = 58,500,851.75

If the quotient is a whole number, then 4 and 58,500,851.75 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:

1 234,003,407
-1 234,003,407
Keep dividing by the next highest number until you cannot divide anymore.

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

11129313193418999,88923,663260,293686,227733,5537,548,4978,069,08321,273,037234,003,407
-1-11-29-31-319-341-899-9,889-23,663-260,293-686,227-733,553-7,548,497-8,069,083-21,273,037-234,003,407

More Examples

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