Q: What are the factor combinations of the number 121,144,345?

 A:
Positive:   1 x 1211443455 x 242288697 x 1730633535 x 3461267331 x 3659951655 x 731992317 x 5228510457 x 11585
Negative: -1 x -121144345-5 x -24228869-7 x -17306335-35 x -3461267-331 x -365995-1655 x -73199-2317 x -52285-10457 x -11585


How do I find the factor combinations of the number 121,144,345?

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 121,144,345, 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.

1 121,144,345
-1 -121,144,345

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 121,144,345.

Example:
1 x 121,144,345 = 121,144,345
and
-1 x -121,144,345 = 121,144,345
Notice both answers equal 121,144,345

With that explanation out of the way, let's continue. Next, we take the number 121,144,345 and divide it by 2:

121,144,345 ÷ 2 = 60,572,172.5

If the quotient is a whole number, then 2 and 60,572,172.5 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:

1 121,144,345
-1 -121,144,345

Now, we try dividing 121,144,345 by 3:

121,144,345 ÷ 3 = 40,381,448.3333

If the quotient is a whole number, then 3 and 40,381,448.3333 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:

1 121,144,345
-1 -121,144,345

Let's try dividing by 4:

121,144,345 ÷ 4 = 30,286,086.25

If the quotient is a whole number, then 4 and 30,286,086.25 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:

1 121,144,345
-1 121,144,345
Keep dividing by the next highest number until you cannot divide anymore.

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

157353311,6552,31710,45711,58552,28573,199365,9953,461,26717,306,33524,228,869121,144,345
-1-5-7-35-331-1,655-2,317-10,457-11,585-52,285-73,199-365,995-3,461,267-17,306,335-24,228,869-121,144,345

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