Q: What are the factor combinations of the number 689,185?

 A:
Positive:   1 x 6891855 x 1378377 x 9845529 x 2376535 x 1969149 x 1406597 x 7105145 x 4753203 x 3395245 x 2813485 x 1421679 x 1015
Negative: -1 x -689185-5 x -137837-7 x -98455-29 x -23765-35 x -19691-49 x -14065-97 x -7105-145 x -4753-203 x -3395-245 x -2813-485 x -1421-679 x -1015


How do I find the factor combinations of the number 689,185?

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 689,185, 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.

1 689,185
-1 -689,185

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 689,185.

Example:
1 x 689,185 = 689,185
and
-1 x -689,185 = 689,185
Notice both answers equal 689,185

With that explanation out of the way, let's continue. Next, we take the number 689,185 and divide it by 2:

689,185 ÷ 2 = 344,592.5

If the quotient is a whole number, then 2 and 344,592.5 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:

1 689,185
-1 -689,185

Now, we try dividing 689,185 by 3:

689,185 ÷ 3 = 229,728.3333

If the quotient is a whole number, then 3 and 229,728.3333 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:

1 689,185
-1 -689,185

Let's try dividing by 4:

689,185 ÷ 4 = 172,296.25

If the quotient is a whole number, then 4 and 172,296.25 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:

1 689,185
-1 689,185
Keep dividing by the next highest number until you cannot divide anymore.

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

157293549971452032454856791,0151,4212,8133,3954,7537,10514,06519,69123,76598,455137,837689,185
-1-5-7-29-35-49-97-145-203-245-485-679-1,015-1,421-2,813-3,395-4,753-7,105-14,065-19,691-23,765-98,455-137,837-689,185

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