Q: What are the factor combinations of the number 1,254,125?

 A:
Positive:   1 x 12541255 x 25082525 x 5016579 x 15875125 x 10033127 x 9875395 x 3175635 x 1975
Negative: -1 x -1254125-5 x -250825-25 x -50165-79 x -15875-125 x -10033-127 x -9875-395 x -3175-635 x -1975


How do I find the factor combinations of the number 1,254,125?

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 1,254,125, 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 1,254,125
-1 -1,254,125

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 1,254,125.

Example:
1 x 1,254,125 = 1,254,125
and
-1 x -1,254,125 = 1,254,125
Notice both answers equal 1,254,125

With that explanation out of the way, let's continue. Next, we take the number 1,254,125 and divide it by 2:

1,254,125 ÷ 2 = 627,062.5

If the quotient is a whole number, then 2 and 627,062.5 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 1,254,125
-1 -1,254,125

Now, we try dividing 1,254,125 by 3:

1,254,125 ÷ 3 = 418,041.6667

If the quotient is a whole number, then 3 and 418,041.6667 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 1,254,125
-1 -1,254,125

Let's try dividing by 4:

1,254,125 ÷ 4 = 313,531.25

If the quotient is a whole number, then 4 and 313,531.25 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 1,254,125
-1 1,254,125
Keep dividing by the next highest number until you cannot divide anymore.

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

1525791251273956351,9753,1759,87510,03315,87550,165250,8251,254,125
-1-5-25-79-125-127-395-635-1,975-3,175-9,875-10,033-15,875-50,165-250,825-1,254,125

More Examples

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