Q: What are the factor combinations of the number 122,213,333?

 A:
Positive:   1 x 12221333311 x 1111030341 x 2980813101 x 1210033451 x 2709831111 x 1100032683 x 455514141 x 29513
Negative: -1 x -122213333-11 x -11110303-41 x -2980813-101 x -1210033-451 x -270983-1111 x -110003-2683 x -45551-4141 x -29513


How do I find the factor combinations of the number 122,213,333?

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 122,213,333, 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.

1 122,213,333
-1 -122,213,333

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 122,213,333.

Example:
1 x 122,213,333 = 122,213,333
and
-1 x -122,213,333 = 122,213,333
Notice both answers equal 122,213,333

With that explanation out of the way, let's continue. Next, we take the number 122,213,333 and divide it by 2:

122,213,333 ÷ 2 = 61,106,666.5

If the quotient is a whole number, then 2 and 61,106,666.5 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:

1 122,213,333
-1 -122,213,333

Now, we try dividing 122,213,333 by 3:

122,213,333 ÷ 3 = 40,737,777.6667

If the quotient is a whole number, then 3 and 40,737,777.6667 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:

1 122,213,333
-1 -122,213,333

Let's try dividing by 4:

122,213,333 ÷ 4 = 30,553,333.25

If the quotient is a whole number, then 4 and 30,553,333.25 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:

1 122,213,333
-1 122,213,333
Keep dividing by the next highest number until you cannot divide anymore.

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

111411014511,1112,6834,14129,51345,551110,003270,9831,210,0332,980,81311,110,303122,213,333
-1-11-41-101-451-1,111-2,683-4,141-29,513-45,551-110,003-270,983-1,210,033-2,980,813-11,110,303-122,213,333

More Examples

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