Q: What are the factor combinations of the number 31,222,433?

 A:
Positive:   1 x 3122243311 x 2838403101 x 309133157 x 198869179 x 1744271111 x 281031727 x 180791969 x 15857
Negative: -1 x -31222433-11 x -2838403-101 x -309133-157 x -198869-179 x -174427-1111 x -28103-1727 x -18079-1969 x -15857


How do I find the factor combinations of the number 31,222,433?

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 31,222,433, 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 31,222,433
-1 -31,222,433

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 31,222,433.

Example:
1 x 31,222,433 = 31,222,433
and
-1 x -31,222,433 = 31,222,433
Notice both answers equal 31,222,433

With that explanation out of the way, let's continue. Next, we take the number 31,222,433 and divide it by 2:

31,222,433 ÷ 2 = 15,611,216.5

If the quotient is a whole number, then 2 and 15,611,216.5 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 31,222,433
-1 -31,222,433

Now, we try dividing 31,222,433 by 3:

31,222,433 ÷ 3 = 10,407,477.6667

If the quotient is a whole number, then 3 and 10,407,477.6667 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 31,222,433
-1 -31,222,433

Let's try dividing by 4:

31,222,433 ÷ 4 = 7,805,608.25

If the quotient is a whole number, then 4 and 7,805,608.25 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 31,222,433
-1 31,222,433
Keep dividing by the next highest number until you cannot divide anymore.

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

1111011571791,1111,7271,96915,85718,07928,103174,427198,869309,1332,838,40331,222,433
-1-11-101-157-179-1,111-1,727-1,969-15,857-18,079-28,103-174,427-198,869-309,133-2,838,403-31,222,433

More Examples

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