Q: What are the factor combinations of the number 31,948,105?

 A:
Positive:   1 x 319481055 x 63896217 x 456401535 x 912803769 x 415451187 x 269153845 x 83095383 x 5935
Negative: -1 x -31948105-5 x -6389621-7 x -4564015-35 x -912803-769 x -41545-1187 x -26915-3845 x -8309-5383 x -5935


How do I find the factor combinations of the number 31,948,105?

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 31,948,105, 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 31,948,105
-1 -31,948,105

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 31,948,105.

Example:
1 x 31,948,105 = 31,948,105
and
-1 x -31,948,105 = 31,948,105
Notice both answers equal 31,948,105

With that explanation out of the way, let's continue. Next, we take the number 31,948,105 and divide it by 2:

31,948,105 ÷ 2 = 15,974,052.5

If the quotient is a whole number, then 2 and 15,974,052.5 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 31,948,105
-1 -31,948,105

Now, we try dividing 31,948,105 by 3:

31,948,105 ÷ 3 = 10,649,368.3333

If the quotient is a whole number, then 3 and 10,649,368.3333 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 31,948,105
-1 -31,948,105

Let's try dividing by 4:

31,948,105 ÷ 4 = 7,987,026.25

If the quotient is a whole number, then 4 and 7,987,026.25 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 31,948,105
-1 31,948,105
Keep dividing by the next highest number until you cannot divide anymore.

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

157357691,1873,8455,3835,9358,30926,91541,545912,8034,564,0156,389,62131,948,105
-1-5-7-35-769-1,187-3,845-5,383-5,935-8,309-26,915-41,545-912,803-4,564,015-6,389,621-31,948,105

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