Q: What are the factor combinations of the number 344,267?

 A:
Positive:   1 x 3442677 x 4918111 x 3129717 x 2025177 x 4471119 x 2893187 x 1841263 x 1309
Negative: -1 x -344267-7 x -49181-11 x -31297-17 x -20251-77 x -4471-119 x -2893-187 x -1841-263 x -1309


How do I find the factor combinations of the number 344,267?

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 344,267, 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.

1 344,267
-1 -344,267

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 344,267.

Example:
1 x 344,267 = 344,267
and
-1 x -344,267 = 344,267
Notice both answers equal 344,267

With that explanation out of the way, let's continue. Next, we take the number 344,267 and divide it by 2:

344,267 ÷ 2 = 172,133.5

If the quotient is a whole number, then 2 and 172,133.5 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:

1 344,267
-1 -344,267

Now, we try dividing 344,267 by 3:

344,267 ÷ 3 = 114,755.6667

If the quotient is a whole number, then 3 and 114,755.6667 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:

1 344,267
-1 -344,267

Let's try dividing by 4:

344,267 ÷ 4 = 86,066.75

If the quotient is a whole number, then 4 and 86,066.75 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:

1 344,267
-1 344,267
Keep dividing by the next highest number until you cannot divide anymore.

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

171117771191872631,3091,8412,8934,47120,25131,29749,181344,267
-1-7-11-17-77-119-187-263-1,309-1,841-2,893-4,471-20,251-31,297-49,181-344,267

More Examples

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