Q: What are the factor combinations of the number 5,300,125?

 A:
Positive:   1 x 53001255 x 106002525 x 212005109 x 48625125 x 42401389 x 13625545 x 97251945 x 2725
Negative: -1 x -5300125-5 x -1060025-25 x -212005-109 x -48625-125 x -42401-389 x -13625-545 x -9725-1945 x -2725


How do I find the factor combinations of the number 5,300,125?

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 5,300,125, 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 5,300,125
-1 -5,300,125

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 5,300,125.

Example:
1 x 5,300,125 = 5,300,125
and
-1 x -5,300,125 = 5,300,125
Notice both answers equal 5,300,125

With that explanation out of the way, let's continue. Next, we take the number 5,300,125 and divide it by 2:

5,300,125 ÷ 2 = 2,650,062.5

If the quotient is a whole number, then 2 and 2,650,062.5 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 5,300,125
-1 -5,300,125

Now, we try dividing 5,300,125 by 3:

5,300,125 ÷ 3 = 1,766,708.3333

If the quotient is a whole number, then 3 and 1,766,708.3333 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 5,300,125
-1 -5,300,125

Let's try dividing by 4:

5,300,125 ÷ 4 = 1,325,031.25

If the quotient is a whole number, then 4 and 1,325,031.25 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 5,300,125
-1 5,300,125
Keep dividing by the next highest number until you cannot divide anymore.

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

15251091253895451,9452,7259,72513,62542,40148,625212,0051,060,0255,300,125
-1-5-25-109-125-389-545-1,945-2,725-9,725-13,625-42,401-48,625-212,005-1,060,025-5,300,125

More Examples

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