Q: What are the factor combinations of the number 126,635?

 A:
Positive:   1 x 1266355 x 2532719 x 666531 x 408543 x 294595 x 1333155 x 817215 x 589
Negative: -1 x -126635-5 x -25327-19 x -6665-31 x -4085-43 x -2945-95 x -1333-155 x -817-215 x -589


How do I find the factor combinations of the number 126,635?

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 126,635, 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.

1 126,635
-1 -126,635

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 126,635.

Example:
1 x 126,635 = 126,635
and
-1 x -126,635 = 126,635
Notice both answers equal 126,635

With that explanation out of the way, let's continue. Next, we take the number 126,635 and divide it by 2:

126,635 ÷ 2 = 63,317.5

If the quotient is a whole number, then 2 and 63,317.5 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:

1 126,635
-1 -126,635

Now, we try dividing 126,635 by 3:

126,635 ÷ 3 = 42,211.6667

If the quotient is a whole number, then 3 and 42,211.6667 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:

1 126,635
-1 -126,635

Let's try dividing by 4:

126,635 ÷ 4 = 31,658.75

If the quotient is a whole number, then 4 and 31,658.75 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:

1 126,635
-1 126,635
Keep dividing by the next highest number until you cannot divide anymore.

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

15193143951552155898171,3332,9454,0856,66525,327126,635
-1-5-19-31-43-95-155-215-589-817-1,333-2,945-4,085-6,665-25,327-126,635

More Examples

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