Q: What are the factor combinations of the number 3,101,105?

 A:
Positive:   1 x 31011055 x 6202217 x 44301535 x 88603251 x 12355353 x 87851255 x 24711757 x 1765
Negative: -1 x -3101105-5 x -620221-7 x -443015-35 x -88603-251 x -12355-353 x -8785-1255 x -2471-1757 x -1765


How do I find the factor combinations of the number 3,101,105?

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 3,101,105, 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 3,101,105
-1 -3,101,105

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 3,101,105.

Example:
1 x 3,101,105 = 3,101,105
and
-1 x -3,101,105 = 3,101,105
Notice both answers equal 3,101,105

With that explanation out of the way, let's continue. Next, we take the number 3,101,105 and divide it by 2:

3,101,105 ÷ 2 = 1,550,552.5

If the quotient is a whole number, then 2 and 1,550,552.5 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 3,101,105
-1 -3,101,105

Now, we try dividing 3,101,105 by 3:

3,101,105 ÷ 3 = 1,033,701.6667

If the quotient is a whole number, then 3 and 1,033,701.6667 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 3,101,105
-1 -3,101,105

Let's try dividing by 4:

3,101,105 ÷ 4 = 775,276.25

If the quotient is a whole number, then 4 and 775,276.25 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 3,101,105
-1 3,101,105
Keep dividing by the next highest number until you cannot divide anymore.

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

157352513531,2551,7571,7652,4718,78512,35588,603443,015620,2213,101,105
-1-5-7-35-251-353-1,255-1,757-1,765-2,471-8,785-12,355-88,603-443,015-620,221-3,101,105

More Examples

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