Q: What are the factor combinations of the number 31,761,235?

 A:
Positive:   1 x 317612355 x 635224711 x 288738529 x 109521555 x 577477145 x 219043319 x 995651595 x 19913
Negative: -1 x -31761235-5 x -6352247-11 x -2887385-29 x -1095215-55 x -577477-145 x -219043-319 x -99565-1595 x -19913


How do I find the factor combinations of the number 31,761,235?

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 31,761,235, 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 31,761,235
-1 -31,761,235

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 31,761,235.

Example:
1 x 31,761,235 = 31,761,235
and
-1 x -31,761,235 = 31,761,235
Notice both answers equal 31,761,235

With that explanation out of the way, let's continue. Next, we take the number 31,761,235 and divide it by 2:

31,761,235 ÷ 2 = 15,880,617.5

If the quotient is a whole number, then 2 and 15,880,617.5 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 31,761,235
-1 -31,761,235

Now, we try dividing 31,761,235 by 3:

31,761,235 ÷ 3 = 10,587,078.3333

If the quotient is a whole number, then 3 and 10,587,078.3333 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 31,761,235
-1 -31,761,235

Let's try dividing by 4:

31,761,235 ÷ 4 = 7,940,308.75

If the quotient is a whole number, then 4 and 7,940,308.75 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 31,761,235
-1 31,761,235
Keep dividing by the next highest number until you cannot divide anymore.

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

151129551453191,59519,91399,565219,043577,4771,095,2152,887,3856,352,24731,761,235
-1-5-11-29-55-145-319-1,595-19,913-99,565-219,043-577,477-1,095,215-2,887,385-6,352,247-31,761,235

More Examples

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