Q: What are the factor combinations of the number 667,221,613?

 A:
Positive:   1 x 66722161319 x 35116927167 x 3995339439 x 1519867479 x 13929473173 x 2102818341 x 799939101 x 73313
Negative: -1 x -667221613-19 x -35116927-167 x -3995339-439 x -1519867-479 x -1392947-3173 x -210281-8341 x -79993-9101 x -73313


How do I find the factor combinations of the number 667,221,613?

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 667,221,613, 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.

1 667,221,613
-1 -667,221,613

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 667,221,613.

Example:
1 x 667,221,613 = 667,221,613
and
-1 x -667,221,613 = 667,221,613
Notice both answers equal 667,221,613

With that explanation out of the way, let's continue. Next, we take the number 667,221,613 and divide it by 2:

667,221,613 ÷ 2 = 333,610,806.5

If the quotient is a whole number, then 2 and 333,610,806.5 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:

1 667,221,613
-1 -667,221,613

Now, we try dividing 667,221,613 by 3:

667,221,613 ÷ 3 = 222,407,204.3333

If the quotient is a whole number, then 3 and 222,407,204.3333 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:

1 667,221,613
-1 -667,221,613

Let's try dividing by 4:

667,221,613 ÷ 4 = 166,805,403.25

If the quotient is a whole number, then 4 and 166,805,403.25 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:

1 667,221,613
-1 667,221,613
Keep dividing by the next highest number until you cannot divide anymore.

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

1191674394793,1738,3419,10173,31379,993210,2811,392,9471,519,8673,995,33935,116,927667,221,613
-1-19-167-439-479-3,173-8,341-9,101-73,313-79,993-210,281-1,392,947-1,519,867-3,995,339-35,116,927-667,221,613

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