Q: What are the factor combinations of the number 689,095?

 A:
Positive:   1 x 6890955 x 13781911 x 6264517 x 4053555 x 1252967 x 1028585 x 8107121 x 5695187 x 3685335 x 2057605 x 1139737 x 935
Negative: -1 x -689095-5 x -137819-11 x -62645-17 x -40535-55 x -12529-67 x -10285-85 x -8107-121 x -5695-187 x -3685-335 x -2057-605 x -1139-737 x -935


How do I find the factor combinations of the number 689,095?

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 689,095, 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.

1 689,095
-1 -689,095

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 689,095.

Example:
1 x 689,095 = 689,095
and
-1 x -689,095 = 689,095
Notice both answers equal 689,095

With that explanation out of the way, let's continue. Next, we take the number 689,095 and divide it by 2:

689,095 ÷ 2 = 344,547.5

If the quotient is a whole number, then 2 and 344,547.5 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:

1 689,095
-1 -689,095

Now, we try dividing 689,095 by 3:

689,095 ÷ 3 = 229,698.3333

If the quotient is a whole number, then 3 and 229,698.3333 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:

1 689,095
-1 -689,095

Let's try dividing by 4:

689,095 ÷ 4 = 172,273.75

If the quotient is a whole number, then 4 and 172,273.75 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:

1 689,095
-1 689,095
Keep dividing by the next highest number until you cannot divide anymore.

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

1511175567851211873356057379351,1392,0573,6855,6958,10710,28512,52940,53562,645137,819689,095
-1-5-11-17-55-67-85-121-187-335-605-737-935-1,139-2,057-3,685-5,695-8,107-10,285-12,529-40,535-62,645-137,819-689,095

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