Q: What are the factor combinations of the number 121,606,117?

 A:
Positive:   1 x 12160611717 x 7153301181 x 6718573077 x 39521
Negative: -1 x -121606117-17 x -7153301-181 x -671857-3077 x -39521


How do I find the factor combinations of the number 121,606,117?

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 121,606,117, 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.

1 121,606,117
-1 -121,606,117

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 121,606,117.

Example:
1 x 121,606,117 = 121,606,117
and
-1 x -121,606,117 = 121,606,117
Notice both answers equal 121,606,117

With that explanation out of the way, let's continue. Next, we take the number 121,606,117 and divide it by 2:

121,606,117 ÷ 2 = 60,803,058.5

If the quotient is a whole number, then 2 and 60,803,058.5 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:

1 121,606,117
-1 -121,606,117

Now, we try dividing 121,606,117 by 3:

121,606,117 ÷ 3 = 40,535,372.3333

If the quotient is a whole number, then 3 and 40,535,372.3333 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:

1 121,606,117
-1 -121,606,117

Let's try dividing by 4:

121,606,117 ÷ 4 = 30,401,529.25

If the quotient is a whole number, then 4 and 30,401,529.25 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:

1 121,606,117
-1 121,606,117
Keep dividing by the next highest number until you cannot divide anymore.

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

1171813,07739,521671,8577,153,301121,606,117
-1-17-181-3,077-39,521-671,857-7,153,301-121,606,117

More Examples

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