Q: What are the factor combinations of the number 222,121,135?

 A:
Positive:   1 x 2221211355 x 4442422759 x 3764765295 x 752953643 x 3454451171 x 1896853215 x 690895855 x 37937
Negative: -1 x -222121135-5 x -44424227-59 x -3764765-295 x -752953-643 x -345445-1171 x -189685-3215 x -69089-5855 x -37937


How do I find the factor combinations of the number 222,121,135?

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 222,121,135, 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.

1 222,121,135
-1 -222,121,135

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 222,121,135.

Example:
1 x 222,121,135 = 222,121,135
and
-1 x -222,121,135 = 222,121,135
Notice both answers equal 222,121,135

With that explanation out of the way, let's continue. Next, we take the number 222,121,135 and divide it by 2:

222,121,135 ÷ 2 = 111,060,567.5

If the quotient is a whole number, then 2 and 111,060,567.5 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:

1 222,121,135
-1 -222,121,135

Now, we try dividing 222,121,135 by 3:

222,121,135 ÷ 3 = 74,040,378.3333

If the quotient is a whole number, then 3 and 74,040,378.3333 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:

1 222,121,135
-1 -222,121,135

Let's try dividing by 4:

222,121,135 ÷ 4 = 55,530,283.75

If the quotient is a whole number, then 4 and 55,530,283.75 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:

1 222,121,135
-1 222,121,135
Keep dividing by the next highest number until you cannot divide anymore.

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

15592956431,1713,2155,85537,93769,089189,685345,445752,9533,764,76544,424,227222,121,135
-1-5-59-295-643-1,171-3,215-5,855-37,937-69,089-189,685-345,445-752,953-3,764,765-44,424,227-222,121,135

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