Q: What are the factor combinations of the number 4,421,125?

 A:
Positive:   1 x 44211255 x 88422525 x 176845113 x 39125125 x 35369313 x 14125565 x 78251565 x 2825
Negative: -1 x -4421125-5 x -884225-25 x -176845-113 x -39125-125 x -35369-313 x -14125-565 x -7825-1565 x -2825


How do I find the factor combinations of the number 4,421,125?

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 4,421,125, 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 4,421,125
-1 -4,421,125

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 4,421,125.

Example:
1 x 4,421,125 = 4,421,125
and
-1 x -4,421,125 = 4,421,125
Notice both answers equal 4,421,125

With that explanation out of the way, let's continue. Next, we take the number 4,421,125 and divide it by 2:

4,421,125 ÷ 2 = 2,210,562.5

If the quotient is a whole number, then 2 and 2,210,562.5 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 4,421,125
-1 -4,421,125

Now, we try dividing 4,421,125 by 3:

4,421,125 ÷ 3 = 1,473,708.3333

If the quotient is a whole number, then 3 and 1,473,708.3333 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 4,421,125
-1 -4,421,125

Let's try dividing by 4:

4,421,125 ÷ 4 = 1,105,281.25

If the quotient is a whole number, then 4 and 1,105,281.25 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 4,421,125
-1 4,421,125
Keep dividing by the next highest number until you cannot divide anymore.

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

15251131253135651,5652,8257,82514,12535,36939,125176,845884,2254,421,125
-1-5-25-113-125-313-565-1,565-2,825-7,825-14,125-35,369-39,125-176,845-884,225-4,421,125

More Examples

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