Q: What are the factor combinations of the number 4,004,345?

 A:
Positive:   1 x 40043455 x 80086919 x 21075561 x 6564595 x 42151305 x 13129691 x 57951159 x 3455
Negative: -1 x -4004345-5 x -800869-19 x -210755-61 x -65645-95 x -42151-305 x -13129-691 x -5795-1159 x -3455


How do I find the factor combinations of the number 4,004,345?

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 4,004,345, 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 4,004,345
-1 -4,004,345

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 4,004,345.

Example:
1 x 4,004,345 = 4,004,345
and
-1 x -4,004,345 = 4,004,345
Notice both answers equal 4,004,345

With that explanation out of the way, let's continue. Next, we take the number 4,004,345 and divide it by 2:

4,004,345 ÷ 2 = 2,002,172.5

If the quotient is a whole number, then 2 and 2,002,172.5 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 4,004,345
-1 -4,004,345

Now, we try dividing 4,004,345 by 3:

4,004,345 ÷ 3 = 1,334,781.6667

If the quotient is a whole number, then 3 and 1,334,781.6667 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 4,004,345
-1 -4,004,345

Let's try dividing by 4:

4,004,345 ÷ 4 = 1,001,086.25

If the quotient is a whole number, then 4 and 1,001,086.25 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 4,004,345
-1 4,004,345
Keep dividing by the next highest number until you cannot divide anymore.

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

151961953056911,1593,4555,79513,12942,15165,645210,755800,8694,004,345
-1-5-19-61-95-305-691-1,159-3,455-5,795-13,129-42,151-65,645-210,755-800,869-4,004,345

More Examples

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