Q: What are the factor combinations of the number 421,219?
A:
Positive:
1 x 421219281 x 1499
Negative:
-1 x -421219-281 x -1499
A:
Positive:
1 x 421219281 x 1499
Negative:
-1 x -421219-281 x -1499
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 421,219, 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 | 421,219 | |
-1 | -421,219 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 421,219.
Example:
1 x 421,219 = 421,219
and
-1 x -421,219 = 421,219
Notice both answers equal 421,219
With that explanation out of the way, let's continue. Next, we take the number 421,219 and divide it by 2:
421,219 ÷ 2 = 210,609.5
If the quotient is a whole number, then 2 and 210,609.5 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 | 421,219 | |
-1 | -421,219 |
Now, we try dividing 421,219 by 3:
421,219 ÷ 3 = 140,406.3333
If the quotient is a whole number, then 3 and 140,406.3333 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 | 421,219 | |
-1 | -421,219 |
Let's try dividing by 4:
421,219 ÷ 4 = 105,304.75
If the quotient is a whole number, then 4 and 105,304.75 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 | 421,219 | |
-1 | 421,219 |
If you did it right, you will end up with this table:
1 | 281 | 1,499 | 421,219 |
-1 | -281 | -1,499 | -421,219 |
Here are some more numbers to try:
Try the factor calculator