Q: What are the factor combinations of the number 21,565?
A:
Positive:
1 x 215655 x 431319 x 113595 x 227
Negative:
-1 x -21565-5 x -4313-19 x -1135-95 x -227
A:
Positive:
1 x 215655 x 431319 x 113595 x 227
Negative:
-1 x -21565-5 x -4313-19 x -1135-95 x -227
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 21,565, it is easier to work with a table - it's called factoring from the outside in.
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 | 21,565 | |
-1 | -21,565 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 21,565.
Example:
1 x 21,565 = 21,565
and
-1 x -21,565 = 21,565
Notice both answers equal 21,565
With that explanation out of the way, let's continue. Next, we take the number 21,565 and divide it by 2:
21,565 ÷ 2 = 10,782.5
If the quotient is a whole number, then 2 and 10,782.5 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 | 21,565 | |
-1 | -21,565 |
Now, we try dividing 21,565 by 3:
21,565 ÷ 3 = 7,188.3333
If the quotient is a whole number, then 3 and 7,188.3333 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 | 21,565 | |
-1 | -21,565 |
Let's try dividing by 4:
21,565 ÷ 4 = 5,391.25
If the quotient is a whole number, then 4 and 5,391.25 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 | 21,565 | |
-1 | 21,565 |
If you did it right, you will end up with this table:
1 | 5 | 19 | 95 | 227 | 1,135 | 4,313 | 21,565 |
-1 | -5 | -19 | -95 | -227 | -1,135 | -4,313 | -21,565 |
Here are some more numbers to try:
Try the factor calculator