Q: What are the factor combinations of the number 1,052,125?

 A:
Positive:   1 x 10521255 x 21042519 x 5537525 x 4208595 x 11075125 x 8417443 x 2375475 x 2215
Negative: -1 x -1052125-5 x -210425-19 x -55375-25 x -42085-95 x -11075-125 x -8417-443 x -2375-475 x -2215


How do I find the factor combinations of the number 1,052,125?

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 1,052,125, 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 1,052,125
-1 -1,052,125

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 1,052,125.

Example:
1 x 1,052,125 = 1,052,125
and
-1 x -1,052,125 = 1,052,125
Notice both answers equal 1,052,125

With that explanation out of the way, let's continue. Next, we take the number 1,052,125 and divide it by 2:

1,052,125 ÷ 2 = 526,062.5

If the quotient is a whole number, then 2 and 526,062.5 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 1,052,125
-1 -1,052,125

Now, we try dividing 1,052,125 by 3:

1,052,125 ÷ 3 = 350,708.3333

If the quotient is a whole number, then 3 and 350,708.3333 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 1,052,125
-1 -1,052,125

Let's try dividing by 4:

1,052,125 ÷ 4 = 263,031.25

If the quotient is a whole number, then 4 and 263,031.25 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 1,052,125
-1 1,052,125
Keep dividing by the next highest number until you cannot divide anymore.

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

151925951254434752,2152,3758,41711,07542,08555,375210,4251,052,125
-1-5-19-25-95-125-443-475-2,215-2,375-8,417-11,075-42,085-55,375-210,425-1,052,125

More Examples

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