Q: What are the factor combinations of the number 31,151,735?

 A:
Positive:   1 x 311517355 x 623034717 x 183245519 x 163956585 x 36649195 x 327913323 x 964451615 x 19289
Negative: -1 x -31151735-5 x -6230347-17 x -1832455-19 x -1639565-85 x -366491-95 x -327913-323 x -96445-1615 x -19289


How do I find the factor combinations of the number 31,151,735?

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 31,151,735, 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 31,151,735
-1 -31,151,735

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 31,151,735.

Example:
1 x 31,151,735 = 31,151,735
and
-1 x -31,151,735 = 31,151,735
Notice both answers equal 31,151,735

With that explanation out of the way, let's continue. Next, we take the number 31,151,735 and divide it by 2:

31,151,735 ÷ 2 = 15,575,867.5

If the quotient is a whole number, then 2 and 15,575,867.5 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 31,151,735
-1 -31,151,735

Now, we try dividing 31,151,735 by 3:

31,151,735 ÷ 3 = 10,383,911.6667

If the quotient is a whole number, then 3 and 10,383,911.6667 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 31,151,735
-1 -31,151,735

Let's try dividing by 4:

31,151,735 ÷ 4 = 7,787,933.75

If the quotient is a whole number, then 4 and 7,787,933.75 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 31,151,735
-1 31,151,735
Keep dividing by the next highest number until you cannot divide anymore.

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

15171985953231,61519,28996,445327,913366,4911,639,5651,832,4556,230,34731,151,735
-1-5-17-19-85-95-323-1,615-19,289-96,445-327,913-366,491-1,639,565-1,832,455-6,230,347-31,151,735

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