Q: What are the factor combinations of the number 278,137?
A:
Positive:
1 x 27813717 x 16361
Negative:
-1 x -278137-17 x -16361
A:
Positive:
1 x 27813717 x 16361
Negative:
-1 x -278137-17 x -16361
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 278,137, 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 | 278,137 | |
-1 | -278,137 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 278,137.
Example:
1 x 278,137 = 278,137
and
-1 x -278,137 = 278,137
Notice both answers equal 278,137
With that explanation out of the way, let's continue. Next, we take the number 278,137 and divide it by 2:
278,137 ÷ 2 = 139,068.5
If the quotient is a whole number, then 2 and 139,068.5 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 | 278,137 | |
-1 | -278,137 |
Now, we try dividing 278,137 by 3:
278,137 ÷ 3 = 92,712.3333
If the quotient is a whole number, then 3 and 92,712.3333 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 | 278,137 | |
-1 | -278,137 |
Let's try dividing by 4:
278,137 ÷ 4 = 69,534.25
If the quotient is a whole number, then 4 and 69,534.25 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 | 278,137 | |
-1 | 278,137 |
If you did it right, you will end up with this table:
1 | 17 | 16,361 | 278,137 |
-1 | -17 | -16,361 | -278,137 |
Here are some more numbers to try:
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