Q: What are the factor combinations of the number 61,019?

 A:
Positive:   1 x 610197 x 871723 x 2653161 x 379
Negative: -1 x -61019-7 x -8717-23 x -2653-161 x -379


How do I find the factor combinations of the number 61,019?

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 61,019, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

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 61,019
-1 -61,019

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 61,019.

Example:
1 x 61,019 = 61,019
and
-1 x -61,019 = 61,019
Notice both answers equal 61,019

With that explanation out of the way, let's continue. Next, we take the number 61,019 and divide it by 2:

61,019 ÷ 2 = 30,509.5

If the quotient is a whole number, then 2 and 30,509.5 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 61,019
-1 -61,019

Now, we try dividing 61,019 by 3:

61,019 ÷ 3 = 20,339.6667

If the quotient is a whole number, then 3 and 20,339.6667 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 61,019
-1 -61,019

Let's try dividing by 4:

61,019 ÷ 4 = 15,254.75

If the quotient is a whole number, then 4 and 15,254.75 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 61,019
-1 61,019
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

17231613792,6538,71761,019
-1-7-23-161-379-2,653-8,717-61,019

More Examples

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