Q: What are the factor combinations of the number 426,725?

 A:
Positive:   1 x 4267255 x 8534513 x 3282525 x 1706965 x 6565101 x 4225169 x 2525325 x 1313505 x 845
Negative: -1 x -426725-5 x -85345-13 x -32825-25 x -17069-65 x -6565-101 x -4225-169 x -2525-325 x -1313-505 x -845


How do I find the factor combinations of the number 426,725?

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 426,725, 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.

1 426,725
-1 -426,725

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 426,725.

Example:
1 x 426,725 = 426,725
and
-1 x -426,725 = 426,725
Notice both answers equal 426,725

With that explanation out of the way, let's continue. Next, we take the number 426,725 and divide it by 2:

426,725 ÷ 2 = 213,362.5

If the quotient is a whole number, then 2 and 213,362.5 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:

1 426,725
-1 -426,725

Now, we try dividing 426,725 by 3:

426,725 ÷ 3 = 142,241.6667

If the quotient is a whole number, then 3 and 142,241.6667 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:

1 426,725
-1 -426,725

Let's try dividing by 4:

426,725 ÷ 4 = 106,681.25

If the quotient is a whole number, then 4 and 106,681.25 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:

1 426,725
-1 426,725
Keep dividing by the next highest number until you cannot divide anymore.

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

151325651011693255058451,3132,5254,2256,56517,06932,82585,345426,725
-1-5-13-25-65-101-169-325-505-845-1,313-2,525-4,225-6,565-17,069-32,825-85,345-426,725

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