Q: What are the factor combinations of the number 354,507,103?

 A:
Positive:   1 x 35450710317 x 2085335931 x 11435713113 x 3137231527 x 6726891921 x 1845433503 x 1012015953 x 59551
Negative: -1 x -354507103-17 x -20853359-31 x -11435713-113 x -3137231-527 x -672689-1921 x -184543-3503 x -101201-5953 x -59551


How do I find the factor combinations of the number 354,507,103?

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 354,507,103, 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.

1 354,507,103
-1 -354,507,103

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 354,507,103.

Example:
1 x 354,507,103 = 354,507,103
and
-1 x -354,507,103 = 354,507,103
Notice both answers equal 354,507,103

With that explanation out of the way, let's continue. Next, we take the number 354,507,103 and divide it by 2:

354,507,103 ÷ 2 = 177,253,551.5

If the quotient is a whole number, then 2 and 177,253,551.5 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:

1 354,507,103
-1 -354,507,103

Now, we try dividing 354,507,103 by 3:

354,507,103 ÷ 3 = 118,169,034.3333

If the quotient is a whole number, then 3 and 118,169,034.3333 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:

1 354,507,103
-1 -354,507,103

Let's try dividing by 4:

354,507,103 ÷ 4 = 88,626,775.75

If the quotient is a whole number, then 4 and 88,626,775.75 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:

1 354,507,103
-1 354,507,103
Keep dividing by the next highest number until you cannot divide anymore.

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

117311135271,9213,5035,95359,551101,201184,543672,6893,137,23111,435,71320,853,359354,507,103
-1-17-31-113-527-1,921-3,503-5,953-59,551-101,201-184,543-672,689-3,137,231-11,435,713-20,853,359-354,507,103

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