Q: What are the factor combinations of the number 691,999?

 A:
Positive:   1 x 6919997 x 9885711 x 6290919 x 3642143 x 1609377 x 8987121 x 5719133 x 5203209 x 3311301 x 2299473 x 1463817 x 847
Negative: -1 x -691999-7 x -98857-11 x -62909-19 x -36421-43 x -16093-77 x -8987-121 x -5719-133 x -5203-209 x -3311-301 x -2299-473 x -1463-817 x -847


How do I find the factor combinations of the number 691,999?

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 691,999, 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.

1 691,999
-1 -691,999

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 691,999.

Example:
1 x 691,999 = 691,999
and
-1 x -691,999 = 691,999
Notice both answers equal 691,999

With that explanation out of the way, let's continue. Next, we take the number 691,999 and divide it by 2:

691,999 ÷ 2 = 345,999.5

If the quotient is a whole number, then 2 and 345,999.5 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:

1 691,999
-1 -691,999

Now, we try dividing 691,999 by 3:

691,999 ÷ 3 = 230,666.3333

If the quotient is a whole number, then 3 and 230,666.3333 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:

1 691,999
-1 -691,999

Let's try dividing by 4:

691,999 ÷ 4 = 172,999.75

If the quotient is a whole number, then 4 and 172,999.75 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:

1 691,999
-1 691,999
Keep dividing by the next highest number until you cannot divide anymore.

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

17111943771211332093014738178471,4632,2993,3115,2035,7198,98716,09336,42162,90998,857691,999
-1-7-11-19-43-77-121-133-209-301-473-817-847-1,463-2,299-3,311-5,203-5,719-8,987-16,093-36,421-62,909-98,857-691,999

More Examples

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