Q: What are the factor combinations of the number 296,451,025?

 A:
Positive:   1 x 2964510255 x 5929020513 x 2280392523 x 1288917525 x 1185804165 x 4560785115 x 2577835299 x 991475325 x 912157575 x 5155671495 x 1982957475 x 39659
Negative: -1 x -296451025-5 x -59290205-13 x -22803925-23 x -12889175-25 x -11858041-65 x -4560785-115 x -2577835-299 x -991475-325 x -912157-575 x -515567-1495 x -198295-7475 x -39659


How do I find the factor combinations of the number 296,451,025?

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 296,451,025, 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.

1 296,451,025
-1 -296,451,025

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 296,451,025.

Example:
1 x 296,451,025 = 296,451,025
and
-1 x -296,451,025 = 296,451,025
Notice both answers equal 296,451,025

With that explanation out of the way, let's continue. Next, we take the number 296,451,025 and divide it by 2:

296,451,025 ÷ 2 = 148,225,512.5

If the quotient is a whole number, then 2 and 148,225,512.5 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:

1 296,451,025
-1 -296,451,025

Now, we try dividing 296,451,025 by 3:

296,451,025 ÷ 3 = 98,817,008.3333

If the quotient is a whole number, then 3 and 98,817,008.3333 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:

1 296,451,025
-1 -296,451,025

Let's try dividing by 4:

296,451,025 ÷ 4 = 74,112,756.25

If the quotient is a whole number, then 4 and 74,112,756.25 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:

1 296,451,025
-1 296,451,025
Keep dividing by the next highest number until you cannot divide anymore.

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

15132325651152993255751,4957,47539,659198,295515,567912,157991,4752,577,8354,560,78511,858,04112,889,17522,803,92559,290,205296,451,025
-1-5-13-23-25-65-115-299-325-575-1,495-7,475-39,659-198,295-515,567-912,157-991,475-2,577,835-4,560,785-11,858,041-12,889,175-22,803,925-59,290,205-296,451,025

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