Q: What are the factor combinations of the number 34,231,445?

 A:
Positive:   1 x 342314455 x 684628919 x 180165595 x 360331193 x 177365965 x 354731867 x 183353667 x 9335
Negative: -1 x -34231445-5 x -6846289-19 x -1801655-95 x -360331-193 x -177365-965 x -35473-1867 x -18335-3667 x -9335


How do I find the factor combinations of the number 34,231,445?

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 34,231,445, 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 34,231,445
-1 -34,231,445

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 34,231,445.

Example:
1 x 34,231,445 = 34,231,445
and
-1 x -34,231,445 = 34,231,445
Notice both answers equal 34,231,445

With that explanation out of the way, let's continue. Next, we take the number 34,231,445 and divide it by 2:

34,231,445 ÷ 2 = 17,115,722.5

If the quotient is a whole number, then 2 and 17,115,722.5 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 34,231,445
-1 -34,231,445

Now, we try dividing 34,231,445 by 3:

34,231,445 ÷ 3 = 11,410,481.6667

If the quotient is a whole number, then 3 and 11,410,481.6667 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 34,231,445
-1 -34,231,445

Let's try dividing by 4:

34,231,445 ÷ 4 = 8,557,861.25

If the quotient is a whole number, then 4 and 8,557,861.25 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 34,231,445
-1 34,231,445
Keep dividing by the next highest number until you cannot divide anymore.

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

1519951939651,8673,6679,33518,33535,473177,365360,3311,801,6556,846,28934,231,445
-1-5-19-95-193-965-1,867-3,667-9,335-18,335-35,473-177,365-360,331-1,801,655-6,846,289-34,231,445

More Examples

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