Q: What are the factor combinations of the number 269,675?

 A:
Positive:   1 x 2696755 x 539357 x 3852523 x 1172525 x 1078735 x 770567 x 4025115 x 2345161 x 1675175 x 1541335 x 805469 x 575
Negative: -1 x -269675-5 x -53935-7 x -38525-23 x -11725-25 x -10787-35 x -7705-67 x -4025-115 x -2345-161 x -1675-175 x -1541-335 x -805-469 x -575


How do I find the factor combinations of the number 269,675?

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 269,675, 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.

1 269,675
-1 -269,675

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 269,675.

Example:
1 x 269,675 = 269,675
and
-1 x -269,675 = 269,675
Notice both answers equal 269,675

With that explanation out of the way, let's continue. Next, we take the number 269,675 and divide it by 2:

269,675 ÷ 2 = 134,837.5

If the quotient is a whole number, then 2 and 134,837.5 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:

1 269,675
-1 -269,675

Now, we try dividing 269,675 by 3:

269,675 ÷ 3 = 89,891.6667

If the quotient is a whole number, then 3 and 89,891.6667 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:

1 269,675
-1 -269,675

Let's try dividing by 4:

269,675 ÷ 4 = 67,418.75

If the quotient is a whole number, then 4 and 67,418.75 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:

1 269,675
-1 269,675
Keep dividing by the next highest number until you cannot divide anymore.

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

157232535671151611753354695758051,5411,6752,3454,0257,70510,78711,72538,52553,935269,675
-1-5-7-23-25-35-67-115-161-175-335-469-575-805-1,541-1,675-2,345-4,025-7,705-10,787-11,725-38,525-53,935-269,675

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