Q: What are the factor combinations of the number 140,135,305?

 A:
Positive:   1 x 1401353055 x 28027061109 x 1285645389 x 360245545 x 257129661 x 2120051945 x 720493305 x 42401
Negative: -1 x -140135305-5 x -28027061-109 x -1285645-389 x -360245-545 x -257129-661 x -212005-1945 x -72049-3305 x -42401


How do I find the factor combinations of the number 140,135,305?

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 140,135,305, 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.

1 140,135,305
-1 -140,135,305

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 140,135,305.

Example:
1 x 140,135,305 = 140,135,305
and
-1 x -140,135,305 = 140,135,305
Notice both answers equal 140,135,305

With that explanation out of the way, let's continue. Next, we take the number 140,135,305 and divide it by 2:

140,135,305 ÷ 2 = 70,067,652.5

If the quotient is a whole number, then 2 and 70,067,652.5 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:

1 140,135,305
-1 -140,135,305

Now, we try dividing 140,135,305 by 3:

140,135,305 ÷ 3 = 46,711,768.3333

If the quotient is a whole number, then 3 and 46,711,768.3333 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:

1 140,135,305
-1 -140,135,305

Let's try dividing by 4:

140,135,305 ÷ 4 = 35,033,826.25

If the quotient is a whole number, then 4 and 35,033,826.25 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:

1 140,135,305
-1 140,135,305
Keep dividing by the next highest number until you cannot divide anymore.

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

151093895456611,9453,30542,40172,049212,005257,129360,2451,285,64528,027,061140,135,305
-1-5-109-389-545-661-1,945-3,305-42,401-72,049-212,005-257,129-360,245-1,285,645-28,027,061-140,135,305

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