Q: What are the factor combinations of the number 353,510,135?

 A:
Positive:   1 x 3535101355 x 7070202711 x 3213728555 x 6427457263 x 13441451315 x 2688292893 x 12219514465 x 24439
Negative: -1 x -353510135-5 x -70702027-11 x -32137285-55 x -6427457-263 x -1344145-1315 x -268829-2893 x -122195-14465 x -24439


How do I find the factor combinations of the number 353,510,135?

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 353,510,135, 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.

1 353,510,135
-1 -353,510,135

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 353,510,135.

Example:
1 x 353,510,135 = 353,510,135
and
-1 x -353,510,135 = 353,510,135
Notice both answers equal 353,510,135

With that explanation out of the way, let's continue. Next, we take the number 353,510,135 and divide it by 2:

353,510,135 ÷ 2 = 176,755,067.5

If the quotient is a whole number, then 2 and 176,755,067.5 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:

1 353,510,135
-1 -353,510,135

Now, we try dividing 353,510,135 by 3:

353,510,135 ÷ 3 = 117,836,711.6667

If the quotient is a whole number, then 3 and 117,836,711.6667 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:

1 353,510,135
-1 -353,510,135

Let's try dividing by 4:

353,510,135 ÷ 4 = 88,377,533.75

If the quotient is a whole number, then 4 and 88,377,533.75 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:

1 353,510,135
-1 353,510,135
Keep dividing by the next highest number until you cannot divide anymore.

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

1511552631,3152,89314,46524,439122,195268,8291,344,1456,427,45732,137,28570,702,027353,510,135
-1-5-11-55-263-1,315-2,893-14,465-24,439-122,195-268,829-1,344,145-6,427,457-32,137,285-70,702,027-353,510,135

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