Q: What are the factor combinations of the number 454,525?

 A:
Positive:   1 x 4545255 x 9090525 x 18181
Negative: -1 x -454525-5 x -90905-25 x -18181


How do I find the factor combinations of the number 454,525?

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 454,525, 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.

1 454,525
-1 -454,525

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 454,525.

Example:
1 x 454,525 = 454,525
and
-1 x -454,525 = 454,525
Notice both answers equal 454,525

With that explanation out of the way, let's continue. Next, we take the number 454,525 and divide it by 2:

454,525 ÷ 2 = 227,262.5

If the quotient is a whole number, then 2 and 227,262.5 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:

1 454,525
-1 -454,525

Now, we try dividing 454,525 by 3:

454,525 ÷ 3 = 151,508.3333

If the quotient is a whole number, then 3 and 151,508.3333 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:

1 454,525
-1 -454,525

Let's try dividing by 4:

454,525 ÷ 4 = 113,631.25

If the quotient is a whole number, then 4 and 113,631.25 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:

1 454,525
-1 454,525
Keep dividing by the next highest number until you cannot divide anymore.

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

152518,18190,905454,525
-1-5-25-18,181-90,905-454,525

More Examples

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