Q: What are the factor combinations of the number 351,115,105?

 A:
Positive:   1 x 3511151055 x 7022302111 x 3191955555 x 638391179 x 4444495395 x 888899869 x 4040454345 x 80809
Negative: -1 x -351115105-5 x -70223021-11 x -31919555-55 x -6383911-79 x -4444495-395 x -888899-869 x -404045-4345 x -80809


How do I find the factor combinations of the number 351,115,105?

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 351,115,105, 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.

1 351,115,105
-1 -351,115,105

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 351,115,105.

Example:
1 x 351,115,105 = 351,115,105
and
-1 x -351,115,105 = 351,115,105
Notice both answers equal 351,115,105

With that explanation out of the way, let's continue. Next, we take the number 351,115,105 and divide it by 2:

351,115,105 ÷ 2 = 175,557,552.5

If the quotient is a whole number, then 2 and 175,557,552.5 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:

1 351,115,105
-1 -351,115,105

Now, we try dividing 351,115,105 by 3:

351,115,105 ÷ 3 = 117,038,368.3333

If the quotient is a whole number, then 3 and 117,038,368.3333 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:

1 351,115,105
-1 -351,115,105

Let's try dividing by 4:

351,115,105 ÷ 4 = 87,778,776.25

If the quotient is a whole number, then 4 and 87,778,776.25 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:

1 351,115,105
-1 351,115,105
Keep dividing by the next highest number until you cannot divide anymore.

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

151155793958694,34580,809404,045888,8994,444,4956,383,91131,919,55570,223,021351,115,105
-1-5-11-55-79-395-869-4,345-80,809-404,045-888,899-4,444,495-6,383,911-31,919,555-70,223,021-351,115,105

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