Q: What are the factor combinations of the number 21,575?

 A:
Positive:   1 x 215755 x 431525 x 863
Negative: -1 x -21575-5 x -4315-25 x -863


How do I find the factor combinations of the number 21,575?

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 21,575, 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 21,575
-1 -21,575

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 21,575.

Example:
1 x 21,575 = 21,575
and
-1 x -21,575 = 21,575
Notice both answers equal 21,575

With that explanation out of the way, let's continue. Next, we take the number 21,575 and divide it by 2:

21,575 ÷ 2 = 10,787.5

If the quotient is a whole number, then 2 and 10,787.5 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 21,575
-1 -21,575

Now, we try dividing 21,575 by 3:

21,575 ÷ 3 = 7,191.6667

If the quotient is a whole number, then 3 and 7,191.6667 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 21,575
-1 -21,575

Let's try dividing by 4:

21,575 ÷ 4 = 5,393.75

If the quotient is a whole number, then 4 and 5,393.75 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 21,575
-1 21,575
Keep dividing by the next highest number until you cannot divide anymore.

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

15258634,31521,575
-1-5-25-863-4,315-21,575

More Examples

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