Q: What are the factor combinations of the number 728,302,027?

 A:
Positive:   1 x 72830202729 x 2511386379 x 9219013107 x 68065612291 x 3178972971 x 2451373103 x 2347098453 x 86159
Negative: -1 x -728302027-29 x -25113863-79 x -9219013-107 x -6806561-2291 x -317897-2971 x -245137-3103 x -234709-8453 x -86159


How do I find the factor combinations of the number 728,302,027?

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 728,302,027, 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.

1 728,302,027
-1 -728,302,027

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 728,302,027.

Example:
1 x 728,302,027 = 728,302,027
and
-1 x -728,302,027 = 728,302,027
Notice both answers equal 728,302,027

With that explanation out of the way, let's continue. Next, we take the number 728,302,027 and divide it by 2:

728,302,027 ÷ 2 = 364,151,013.5

If the quotient is a whole number, then 2 and 364,151,013.5 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:

1 728,302,027
-1 -728,302,027

Now, we try dividing 728,302,027 by 3:

728,302,027 ÷ 3 = 242,767,342.3333

If the quotient is a whole number, then 3 and 242,767,342.3333 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:

1 728,302,027
-1 -728,302,027

Let's try dividing by 4:

728,302,027 ÷ 4 = 182,075,506.75

If the quotient is a whole number, then 4 and 182,075,506.75 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:

1 728,302,027
-1 728,302,027
Keep dividing by the next highest number until you cannot divide anymore.

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

129791072,2912,9713,1038,45386,159234,709245,137317,8976,806,5619,219,01325,113,863728,302,027
-1-29-79-107-2,291-2,971-3,103-8,453-86,159-234,709-245,137-317,897-6,806,561-9,219,013-25,113,863-728,302,027

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