Q: What are the factor combinations of the number 422,462,401?

 A:
Positive:   1 x 42246240129 x 1456766941 x 1030396143 x 98247071189 x 3553091247 x 3387831763 x 2396278263 x 51127
Negative: -1 x -422462401-29 x -14567669-41 x -10303961-43 x -9824707-1189 x -355309-1247 x -338783-1763 x -239627-8263 x -51127


How do I find the factor combinations of the number 422,462,401?

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 422,462,401, 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.

1 422,462,401
-1 -422,462,401

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 422,462,401.

Example:
1 x 422,462,401 = 422,462,401
and
-1 x -422,462,401 = 422,462,401
Notice both answers equal 422,462,401

With that explanation out of the way, let's continue. Next, we take the number 422,462,401 and divide it by 2:

422,462,401 ÷ 2 = 211,231,200.5

If the quotient is a whole number, then 2 and 211,231,200.5 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:

1 422,462,401
-1 -422,462,401

Now, we try dividing 422,462,401 by 3:

422,462,401 ÷ 3 = 140,820,800.3333

If the quotient is a whole number, then 3 and 140,820,800.3333 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:

1 422,462,401
-1 -422,462,401

Let's try dividing by 4:

422,462,401 ÷ 4 = 105,615,600.25

If the quotient is a whole number, then 4 and 105,615,600.25 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:

1 422,462,401
-1 422,462,401
Keep dividing by the next highest number until you cannot divide anymore.

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

12941431,1891,2471,7638,26351,127239,627338,783355,3099,824,70710,303,96114,567,669422,462,401
-1-29-41-43-1,189-1,247-1,763-8,263-51,127-239,627-338,783-355,309-9,824,707-10,303,961-14,567,669-422,462,401

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