Q: What are the factor combinations of the number 31,426,633?

 A:
Positive:   1 x 314266337 x 448951929 x 1083677149 x 210917203 x 1548111039 x 302471043 x 301314321 x 7273
Negative: -1 x -31426633-7 x -4489519-29 x -1083677-149 x -210917-203 x -154811-1039 x -30247-1043 x -30131-4321 x -7273


How do I find the factor combinations of the number 31,426,633?

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 31,426,633, 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 31,426,633
-1 -31,426,633

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 31,426,633.

Example:
1 x 31,426,633 = 31,426,633
and
-1 x -31,426,633 = 31,426,633
Notice both answers equal 31,426,633

With that explanation out of the way, let's continue. Next, we take the number 31,426,633 and divide it by 2:

31,426,633 ÷ 2 = 15,713,316.5

If the quotient is a whole number, then 2 and 15,713,316.5 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 31,426,633
-1 -31,426,633

Now, we try dividing 31,426,633 by 3:

31,426,633 ÷ 3 = 10,475,544.3333

If the quotient is a whole number, then 3 and 10,475,544.3333 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 31,426,633
-1 -31,426,633

Let's try dividing by 4:

31,426,633 ÷ 4 = 7,856,658.25

If the quotient is a whole number, then 4 and 7,856,658.25 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 31,426,633
-1 31,426,633
Keep dividing by the next highest number until you cannot divide anymore.

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

17291492031,0391,0434,3217,27330,13130,247154,811210,9171,083,6774,489,51931,426,633
-1-7-29-149-203-1,039-1,043-4,321-7,273-30,131-30,247-154,811-210,917-1,083,677-4,489,519-31,426,633

More Examples

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