Q: What are the factor combinations of the number 914,946?

 A:
Positive:   1 x 9149462 x 4574733 x 3049826 x 152491109 x 8394218 x 4197327 x 2798654 x 1399
Negative: -1 x -914946-2 x -457473-3 x -304982-6 x -152491-109 x -8394-218 x -4197-327 x -2798-654 x -1399


How do I find the factor combinations of the number 914,946?

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 914,946, 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.

1 914,946
-1 -914,946

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 914,946.

Example:
1 x 914,946 = 914,946
and
-1 x -914,946 = 914,946
Notice both answers equal 914,946

With that explanation out of the way, let's continue. Next, we take the number 914,946 and divide it by 2:

914,946 ÷ 2 = 457,473

If the quotient is a whole number, then 2 and 457,473 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 457,473 914,946
-1 -2 -457,473 -914,946

Now, we try dividing 914,946 by 3:

914,946 ÷ 3 = 304,982

If the quotient is a whole number, then 3 and 304,982 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 304,982 457,473 914,946
-1 -2 -3 -304,982 -457,473 -914,946

Let's try dividing by 4:

914,946 ÷ 4 = 228,736.5

If the quotient is a whole number, then 4 and 228,736.5 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 2 3 304,982 457,473 914,946
-1 -2 -3 -304,982 -457,473 914,946
Keep dividing by the next highest number until you cannot divide anymore.

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

12361092183276541,3992,7984,1978,394152,491304,982457,473914,946
-1-2-3-6-109-218-327-654-1,399-2,798-4,197-8,394-152,491-304,982-457,473-914,946

More Examples

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