Q: What are the factor combinations of the number 428,527?

 A:
Positive:   1 x 42852711 x 38957163 x 2629239 x 1793
Negative: -1 x -428527-11 x -38957-163 x -2629-239 x -1793


How do I find the factor combinations of the number 428,527?

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 428,527, 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.

1 428,527
-1 -428,527

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 428,527.

Example:
1 x 428,527 = 428,527
and
-1 x -428,527 = 428,527
Notice both answers equal 428,527

With that explanation out of the way, let's continue. Next, we take the number 428,527 and divide it by 2:

428,527 ÷ 2 = 214,263.5

If the quotient is a whole number, then 2 and 214,263.5 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:

1 428,527
-1 -428,527

Now, we try dividing 428,527 by 3:

428,527 ÷ 3 = 142,842.3333

If the quotient is a whole number, then 3 and 142,842.3333 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:

1 428,527
-1 -428,527

Let's try dividing by 4:

428,527 ÷ 4 = 107,131.75

If the quotient is a whole number, then 4 and 107,131.75 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:

1 428,527
-1 428,527
Keep dividing by the next highest number until you cannot divide anymore.

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

1111632391,7932,62938,957428,527
-1-11-163-239-1,793-2,629-38,957-428,527

More Examples

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