Q: What are the factor combinations of the number 457,681?

 A:
Positive:   1 x 4576817 x 65383151 x 3031433 x 1057
Negative: -1 x -457681-7 x -65383-151 x -3031-433 x -1057


How do I find the factor combinations of the number 457,681?

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 457,681, 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.

1 457,681
-1 -457,681

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 457,681.

Example:
1 x 457,681 = 457,681
and
-1 x -457,681 = 457,681
Notice both answers equal 457,681

With that explanation out of the way, let's continue. Next, we take the number 457,681 and divide it by 2:

457,681 ÷ 2 = 228,840.5

If the quotient is a whole number, then 2 and 228,840.5 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:

1 457,681
-1 -457,681

Now, we try dividing 457,681 by 3:

457,681 ÷ 3 = 152,560.3333

If the quotient is a whole number, then 3 and 152,560.3333 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:

1 457,681
-1 -457,681

Let's try dividing by 4:

457,681 ÷ 4 = 114,420.25

If the quotient is a whole number, then 4 and 114,420.25 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:

1 457,681
-1 457,681
Keep dividing by the next highest number until you cannot divide anymore.

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

171514331,0573,03165,383457,681
-1-7-151-433-1,057-3,031-65,383-457,681

More Examples

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