Q: What are the factor combinations of the number 123,305,735?

 A:
Positive:   1 x 1233057355 x 246611477 x 1761510535 x 3523021709 x 1739153545 x 347834963 x 248454969 x 24815
Negative: -1 x -123305735-5 x -24661147-7 x -17615105-35 x -3523021-709 x -173915-3545 x -34783-4963 x -24845-4969 x -24815


How do I find the factor combinations of the number 123,305,735?

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 123,305,735, 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.

1 123,305,735
-1 -123,305,735

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 123,305,735.

Example:
1 x 123,305,735 = 123,305,735
and
-1 x -123,305,735 = 123,305,735
Notice both answers equal 123,305,735

With that explanation out of the way, let's continue. Next, we take the number 123,305,735 and divide it by 2:

123,305,735 ÷ 2 = 61,652,867.5

If the quotient is a whole number, then 2 and 61,652,867.5 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:

1 123,305,735
-1 -123,305,735

Now, we try dividing 123,305,735 by 3:

123,305,735 ÷ 3 = 41,101,911.6667

If the quotient is a whole number, then 3 and 41,101,911.6667 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:

1 123,305,735
-1 -123,305,735

Let's try dividing by 4:

123,305,735 ÷ 4 = 30,826,433.75

If the quotient is a whole number, then 4 and 30,826,433.75 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:

1 123,305,735
-1 123,305,735
Keep dividing by the next highest number until you cannot divide anymore.

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

157357093,5454,9634,96924,81524,84534,783173,9153,523,02117,615,10524,661,147123,305,735
-1-5-7-35-709-3,545-4,963-4,969-24,815-24,845-34,783-173,915-3,523,021-17,615,105-24,661,147-123,305,735

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