Q: What are the factor combinations of the number 105,889?
A:
Positive:
1 x 1058897 x 1512749 x 2161
Negative:
-1 x -105889-7 x -15127-49 x -2161
A:
Positive:
1 x 1058897 x 1512749 x 2161
Negative:
-1 x -105889-7 x -15127-49 x -2161
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 105,889, 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 | 105,889 | |
-1 | -105,889 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 105,889.
Example:
1 x 105,889 = 105,889
and
-1 x -105,889 = 105,889
Notice both answers equal 105,889
With that explanation out of the way, let's continue. Next, we take the number 105,889 and divide it by 2:
105,889 ÷ 2 = 52,944.5
If the quotient is a whole number, then 2 and 52,944.5 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 | 105,889 | |
-1 | -105,889 |
Now, we try dividing 105,889 by 3:
105,889 ÷ 3 = 35,296.3333
If the quotient is a whole number, then 3 and 35,296.3333 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 | 105,889 | |
-1 | -105,889 |
Let's try dividing by 4:
105,889 ÷ 4 = 26,472.25
If the quotient is a whole number, then 4 and 26,472.25 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 | 105,889 | |
-1 | 105,889 |
If you did it right, you will end up with this table:
1 | 7 | 49 | 2,161 | 15,127 | 105,889 |
-1 | -7 | -49 | -2,161 | -15,127 | -105,889 |
Here are some more numbers to try:
Try the factor calculator