Q: What are the factor combinations of the number 1,304,765?

 A:
Positive:   1 x 13047655 x 2609537 x 18639511 x 11861535 x 3727955 x 2372377 x 16945385 x 3389
Negative: -1 x -1304765-5 x -260953-7 x -186395-11 x -118615-35 x -37279-55 x -23723-77 x -16945-385 x -3389


How do I find the factor combinations of the number 1,304,765?

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 1,304,765, 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 1,304,765
-1 -1,304,765

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 1,304,765.

Example:
1 x 1,304,765 = 1,304,765
and
-1 x -1,304,765 = 1,304,765
Notice both answers equal 1,304,765

With that explanation out of the way, let's continue. Next, we take the number 1,304,765 and divide it by 2:

1,304,765 ÷ 2 = 652,382.5

If the quotient is a whole number, then 2 and 652,382.5 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 1,304,765
-1 -1,304,765

Now, we try dividing 1,304,765 by 3:

1,304,765 ÷ 3 = 434,921.6667

If the quotient is a whole number, then 3 and 434,921.6667 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 1,304,765
-1 -1,304,765

Let's try dividing by 4:

1,304,765 ÷ 4 = 326,191.25

If the quotient is a whole number, then 4 and 326,191.25 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 1,304,765
-1 1,304,765
Keep dividing by the next highest number until you cannot divide anymore.

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

157113555773853,38916,94523,72337,279118,615186,395260,9531,304,765
-1-5-7-11-35-55-77-385-3,389-16,945-23,723-37,279-118,615-186,395-260,953-1,304,765

More Examples

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