Q: What are the factor combinations of the number 310,334,011?

 A:
Positive:   1 x 31033401113 x 2387184719 x 1633336989 x 3486899247 x 1256413361 x 859651743 x 4176771157 x 2682231691 x 1835214693 x 661279659 x 3212914117 x 21983
Negative: -1 x -310334011-13 x -23871847-19 x -16333369-89 x -3486899-247 x -1256413-361 x -859651-743 x -417677-1157 x -268223-1691 x -183521-4693 x -66127-9659 x -32129-14117 x -21983


How do I find the factor combinations of the number 310,334,011?

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 310,334,011, 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.

1 310,334,011
-1 -310,334,011

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 310,334,011.

Example:
1 x 310,334,011 = 310,334,011
and
-1 x -310,334,011 = 310,334,011
Notice both answers equal 310,334,011

With that explanation out of the way, let's continue. Next, we take the number 310,334,011 and divide it by 2:

310,334,011 ÷ 2 = 155,167,005.5

If the quotient is a whole number, then 2 and 155,167,005.5 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:

1 310,334,011
-1 -310,334,011

Now, we try dividing 310,334,011 by 3:

310,334,011 ÷ 3 = 103,444,670.3333

If the quotient is a whole number, then 3 and 103,444,670.3333 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:

1 310,334,011
-1 -310,334,011

Let's try dividing by 4:

310,334,011 ÷ 4 = 77,583,502.75

If the quotient is a whole number, then 4 and 77,583,502.75 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:

1 310,334,011
-1 310,334,011
Keep dividing by the next highest number until you cannot divide anymore.

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

11319892473617431,1571,6914,6939,65914,11721,98332,12966,127183,521268,223417,677859,6511,256,4133,486,89916,333,36923,871,847310,334,011
-1-13-19-89-247-361-743-1,157-1,691-4,693-9,659-14,117-21,983-32,129-66,127-183,521-268,223-417,677-859,651-1,256,413-3,486,899-16,333,369-23,871,847-310,334,011

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