Q: What are the factor combinations of the number 1,403,215?

 A:
Positive:   1 x 14032155 x 28064311 x 12756531 x 4526555 x 25513155 x 9053341 x 4115823 x 1705
Negative: -1 x -1403215-5 x -280643-11 x -127565-31 x -45265-55 x -25513-155 x -9053-341 x -4115-823 x -1705


How do I find the factor combinations of the number 1,403,215?

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 1,403,215, 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 1,403,215
-1 -1,403,215

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 1,403,215.

Example:
1 x 1,403,215 = 1,403,215
and
-1 x -1,403,215 = 1,403,215
Notice both answers equal 1,403,215

With that explanation out of the way, let's continue. Next, we take the number 1,403,215 and divide it by 2:

1,403,215 ÷ 2 = 701,607.5

If the quotient is a whole number, then 2 and 701,607.5 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 1,403,215
-1 -1,403,215

Now, we try dividing 1,403,215 by 3:

1,403,215 ÷ 3 = 467,738.3333

If the quotient is a whole number, then 3 and 467,738.3333 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 1,403,215
-1 -1,403,215

Let's try dividing by 4:

1,403,215 ÷ 4 = 350,803.75

If the quotient is a whole number, then 4 and 350,803.75 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 1,403,215
-1 1,403,215
Keep dividing by the next highest number until you cannot divide anymore.

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

151131551553418231,7054,1159,05325,51345,265127,565280,6431,403,215
-1-5-11-31-55-155-341-823-1,705-4,115-9,053-25,513-45,265-127,565-280,643-1,403,215

More Examples

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