Q: What are the factor combinations of the number 427,525?

 A:
Positive:   1 x 4275255 x 855057 x 6107525 x 1710135 x 1221549 x 8725175 x 2443245 x 1745349 x 1225
Negative: -1 x -427525-5 x -85505-7 x -61075-25 x -17101-35 x -12215-49 x -8725-175 x -2443-245 x -1745-349 x -1225


How do I find the factor combinations of the number 427,525?

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 427,525, 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.

1 427,525
-1 -427,525

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 427,525.

Example:
1 x 427,525 = 427,525
and
-1 x -427,525 = 427,525
Notice both answers equal 427,525

With that explanation out of the way, let's continue. Next, we take the number 427,525 and divide it by 2:

427,525 ÷ 2 = 213,762.5

If the quotient is a whole number, then 2 and 213,762.5 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:

1 427,525
-1 -427,525

Now, we try dividing 427,525 by 3:

427,525 ÷ 3 = 142,508.3333

If the quotient is a whole number, then 3 and 142,508.3333 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:

1 427,525
-1 -427,525

Let's try dividing by 4:

427,525 ÷ 4 = 106,881.25

If the quotient is a whole number, then 4 and 106,881.25 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:

1 427,525
-1 427,525
Keep dividing by the next highest number until you cannot divide anymore.

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

1572535491752453491,2251,7452,4438,72512,21517,10161,07585,505427,525
-1-5-7-25-35-49-175-245-349-1,225-1,745-2,443-8,725-12,215-17,101-61,075-85,505-427,525

More Examples

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