Q: What are the factor combinations of the number 34,443,449?

 A:
Positive:   1 x 3444344931 x 111107971 x 4851192201 x 15649
Negative: -1 x -34443449-31 x -1111079-71 x -485119-2201 x -15649


How do I find the factor combinations of the number 34,443,449?

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 34,443,449, 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 34,443,449
-1 -34,443,449

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 34,443,449.

Example:
1 x 34,443,449 = 34,443,449
and
-1 x -34,443,449 = 34,443,449
Notice both answers equal 34,443,449

With that explanation out of the way, let's continue. Next, we take the number 34,443,449 and divide it by 2:

34,443,449 ÷ 2 = 17,221,724.5

If the quotient is a whole number, then 2 and 17,221,724.5 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 34,443,449
-1 -34,443,449

Now, we try dividing 34,443,449 by 3:

34,443,449 ÷ 3 = 11,481,149.6667

If the quotient is a whole number, then 3 and 11,481,149.6667 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 34,443,449
-1 -34,443,449

Let's try dividing by 4:

34,443,449 ÷ 4 = 8,610,862.25

If the quotient is a whole number, then 4 and 8,610,862.25 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 34,443,449
-1 34,443,449
Keep dividing by the next highest number until you cannot divide anymore.

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

131712,20115,649485,1191,111,07934,443,449
-1-31-71-2,201-15,649-485,119-1,111,079-34,443,449

More Examples

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