Q: What are the factor combinations of the number 1,405,943?

 A:
Positive:   1 x 14059437 x 20084911 x 12781319 x 7399731 x 4535377 x 18259133 x 10571209 x 6727217 x 6479341 x 4123589 x 2387961 x 1463
Negative: -1 x -1405943-7 x -200849-11 x -127813-19 x -73997-31 x -45353-77 x -18259-133 x -10571-209 x -6727-217 x -6479-341 x -4123-589 x -2387-961 x -1463


How do I find the factor combinations of the number 1,405,943?

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 1,405,943, 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 1,405,943
-1 -1,405,943

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 1,405,943.

Example:
1 x 1,405,943 = 1,405,943
and
-1 x -1,405,943 = 1,405,943
Notice both answers equal 1,405,943

With that explanation out of the way, let's continue. Next, we take the number 1,405,943 and divide it by 2:

1,405,943 ÷ 2 = 702,971.5

If the quotient is a whole number, then 2 and 702,971.5 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 1,405,943
-1 -1,405,943

Now, we try dividing 1,405,943 by 3:

1,405,943 ÷ 3 = 468,647.6667

If the quotient is a whole number, then 3 and 468,647.6667 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 1,405,943
-1 -1,405,943

Let's try dividing by 4:

1,405,943 ÷ 4 = 351,485.75

If the quotient is a whole number, then 4 and 351,485.75 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 1,405,943
-1 1,405,943
Keep dividing by the next highest number until you cannot divide anymore.

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

17111931771332092173415899611,4632,3874,1236,4796,72710,57118,25945,35373,997127,813200,8491,405,943
-1-7-11-19-31-77-133-209-217-341-589-961-1,463-2,387-4,123-6,479-6,727-10,571-18,259-45,353-73,997-127,813-200,849-1,405,943

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