Q: What are the factor combinations of the number 34,243?

 A:
Positive:   1 x 3424311 x 3113121 x 283
Negative: -1 x -34243-11 x -3113-121 x -283


How do I find the factor combinations of the number 34,243?

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 34,243, 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 34,243
-1 -34,243

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 34,243.

Example:
1 x 34,243 = 34,243
and
-1 x -34,243 = 34,243
Notice both answers equal 34,243

With that explanation out of the way, let's continue. Next, we take the number 34,243 and divide it by 2:

34,243 ÷ 2 = 17,121.5

If the quotient is a whole number, then 2 and 17,121.5 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 34,243
-1 -34,243

Now, we try dividing 34,243 by 3:

34,243 ÷ 3 = 11,414.3333

If the quotient is a whole number, then 3 and 11,414.3333 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 34,243
-1 -34,243

Let's try dividing by 4:

34,243 ÷ 4 = 8,560.75

If the quotient is a whole number, then 4 and 8,560.75 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 34,243
-1 34,243
Keep dividing by the next highest number until you cannot divide anymore.

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

1111212833,11334,243
-1-11-121-283-3,113-34,243

More Examples

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