Q: What are the factor combinations of the number 121,505,021?

 A:
Positive:   1 x 12150502111 x 1104591123 x 5282827179 x 678799253 x 4802571969 x 617092683 x 452874117 x 29513
Negative: -1 x -121505021-11 x -11045911-23 x -5282827-179 x -678799-253 x -480257-1969 x -61709-2683 x -45287-4117 x -29513


How do I find the factor combinations of the number 121,505,021?

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 121,505,021, 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.

1 121,505,021
-1 -121,505,021

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 121,505,021.

Example:
1 x 121,505,021 = 121,505,021
and
-1 x -121,505,021 = 121,505,021
Notice both answers equal 121,505,021

With that explanation out of the way, let's continue. Next, we take the number 121,505,021 and divide it by 2:

121,505,021 ÷ 2 = 60,752,510.5

If the quotient is a whole number, then 2 and 60,752,510.5 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:

1 121,505,021
-1 -121,505,021

Now, we try dividing 121,505,021 by 3:

121,505,021 ÷ 3 = 40,501,673.6667

If the quotient is a whole number, then 3 and 40,501,673.6667 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:

1 121,505,021
-1 -121,505,021

Let's try dividing by 4:

121,505,021 ÷ 4 = 30,376,255.25

If the quotient is a whole number, then 4 and 30,376,255.25 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:

1 121,505,021
-1 121,505,021
Keep dividing by the next highest number until you cannot divide anymore.

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

111231792531,9692,6834,11729,51345,28761,709480,257678,7995,282,82711,045,911121,505,021
-1-11-23-179-253-1,969-2,683-4,117-29,513-45,287-61,709-480,257-678,799-5,282,827-11,045,911-121,505,021

More Examples

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