Q: What are the factor combinations of the number 977,891?

 A:
Positive:   1 x 97789117 x 5752323 x 4251741 x 2385161 x 16031391 x 2501697 x 1403943 x 1037
Negative: -1 x -977891-17 x -57523-23 x -42517-41 x -23851-61 x -16031-391 x -2501-697 x -1403-943 x -1037


How do I find the factor combinations of the number 977,891?

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 977,891, 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.

1 977,891
-1 -977,891

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 977,891.

Example:
1 x 977,891 = 977,891
and
-1 x -977,891 = 977,891
Notice both answers equal 977,891

With that explanation out of the way, let's continue. Next, we take the number 977,891 and divide it by 2:

977,891 ÷ 2 = 488,945.5

If the quotient is a whole number, then 2 and 488,945.5 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:

1 977,891
-1 -977,891

Now, we try dividing 977,891 by 3:

977,891 ÷ 3 = 325,963.6667

If the quotient is a whole number, then 3 and 325,963.6667 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:

1 977,891
-1 -977,891

Let's try dividing by 4:

977,891 ÷ 4 = 244,472.75

If the quotient is a whole number, then 4 and 244,472.75 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:

1 977,891
-1 977,891
Keep dividing by the next highest number until you cannot divide anymore.

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

1172341613916979431,0371,4032,50116,03123,85142,51757,523977,891
-1-17-23-41-61-391-697-943-1,037-1,403-2,501-16,031-23,851-42,517-57,523-977,891

More Examples

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