Q: What are the factor combinations of the number 21,229?
A:
Positive:
1 x 2122913 x 163323 x 92371 x 299
Negative:
-1 x -21229-13 x -1633-23 x -923-71 x -299
A:
Positive:
1 x 2122913 x 163323 x 92371 x 299
Negative:
-1 x -21229-13 x -1633-23 x -923-71 x -299
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 21,229, 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 | 21,229 | |
-1 | -21,229 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 21,229.
Example:
1 x 21,229 = 21,229
and
-1 x -21,229 = 21,229
Notice both answers equal 21,229
With that explanation out of the way, let's continue. Next, we take the number 21,229 and divide it by 2:
21,229 ÷ 2 = 10,614.5
If the quotient is a whole number, then 2 and 10,614.5 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 | 21,229 | |
-1 | -21,229 |
Now, we try dividing 21,229 by 3:
21,229 ÷ 3 = 7,076.3333
If the quotient is a whole number, then 3 and 7,076.3333 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 | 21,229 | |
-1 | -21,229 |
Let's try dividing by 4:
21,229 ÷ 4 = 5,307.25
If the quotient is a whole number, then 4 and 5,307.25 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 | 21,229 | |
-1 | 21,229 |
If you did it right, you will end up with this table:
1 | 13 | 23 | 71 | 299 | 923 | 1,633 | 21,229 |
-1 | -13 | -23 | -71 | -299 | -923 | -1,633 | -21,229 |
Here are some more numbers to try:
Try the factor calculator