Q: What are the factor combinations of the number 120,172,723?

 A:
Positive:   1 x 12017272311 x 1092479323 x 522490129 x 4143887121 x 993163253 x 474991319 x 376717667 x 1801691489 x 807072783 x 431813509 x 342477337 x 16379
Negative: -1 x -120172723-11 x -10924793-23 x -5224901-29 x -4143887-121 x -993163-253 x -474991-319 x -376717-667 x -180169-1489 x -80707-2783 x -43181-3509 x -34247-7337 x -16379


How do I find the factor combinations of the number 120,172,723?

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 120,172,723, 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.

1 120,172,723
-1 -120,172,723

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 120,172,723.

Example:
1 x 120,172,723 = 120,172,723
and
-1 x -120,172,723 = 120,172,723
Notice both answers equal 120,172,723

With that explanation out of the way, let's continue. Next, we take the number 120,172,723 and divide it by 2:

120,172,723 ÷ 2 = 60,086,361.5

If the quotient is a whole number, then 2 and 60,086,361.5 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:

1 120,172,723
-1 -120,172,723

Now, we try dividing 120,172,723 by 3:

120,172,723 ÷ 3 = 40,057,574.3333

If the quotient is a whole number, then 3 and 40,057,574.3333 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:

1 120,172,723
-1 -120,172,723

Let's try dividing by 4:

120,172,723 ÷ 4 = 30,043,180.75

If the quotient is a whole number, then 4 and 30,043,180.75 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:

1 120,172,723
-1 120,172,723
Keep dividing by the next highest number until you cannot divide anymore.

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

11123291212533196671,4892,7833,5097,33716,37934,24743,18180,707180,169376,717474,991993,1634,143,8875,224,90110,924,793120,172,723
-1-11-23-29-121-253-319-667-1,489-2,783-3,509-7,337-16,379-34,247-43,181-80,707-180,169-376,717-474,991-993,163-4,143,887-5,224,901-10,924,793-120,172,723

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