Q: What are the factor combinations of the number 435,321,529?

 A:
Positive:   1 x 43532152923 x 1892702359 x 7378331149 x 29216211357 x 3207972153 x 2021933427 x 1270278791 x 49519
Negative: -1 x -435321529-23 x -18927023-59 x -7378331-149 x -2921621-1357 x -320797-2153 x -202193-3427 x -127027-8791 x -49519


How do I find the factor combinations of the number 435,321,529?

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 435,321,529, 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.

1 435,321,529
-1 -435,321,529

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 435,321,529.

Example:
1 x 435,321,529 = 435,321,529
and
-1 x -435,321,529 = 435,321,529
Notice both answers equal 435,321,529

With that explanation out of the way, let's continue. Next, we take the number 435,321,529 and divide it by 2:

435,321,529 ÷ 2 = 217,660,764.5

If the quotient is a whole number, then 2 and 217,660,764.5 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:

1 435,321,529
-1 -435,321,529

Now, we try dividing 435,321,529 by 3:

435,321,529 ÷ 3 = 145,107,176.3333

If the quotient is a whole number, then 3 and 145,107,176.3333 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:

1 435,321,529
-1 -435,321,529

Let's try dividing by 4:

435,321,529 ÷ 4 = 108,830,382.25

If the quotient is a whole number, then 4 and 108,830,382.25 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:

1 435,321,529
-1 435,321,529
Keep dividing by the next highest number until you cannot divide anymore.

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

123591491,3572,1533,4278,79149,519127,027202,193320,7972,921,6217,378,33118,927,023435,321,529
-1-23-59-149-1,357-2,153-3,427-8,791-49,519-127,027-202,193-320,797-2,921,621-7,378,331-18,927,023-435,321,529

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