Q: What are the factor combinations of the number 31,223,045?

 A:
Positive:   1 x 312230455 x 62446097 x 446043531 x 100719535 x 89208749 x 637205155 x 201439217 x 143885245 x 1274411085 x 287771519 x 205554111 x 7595
Negative: -1 x -31223045-5 x -6244609-7 x -4460435-31 x -1007195-35 x -892087-49 x -637205-155 x -201439-217 x -143885-245 x -127441-1085 x -28777-1519 x -20555-4111 x -7595


How do I find the factor combinations of the number 31,223,045?

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 31,223,045, 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 31,223,045
-1 -31,223,045

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 31,223,045.

Example:
1 x 31,223,045 = 31,223,045
and
-1 x -31,223,045 = 31,223,045
Notice both answers equal 31,223,045

With that explanation out of the way, let's continue. Next, we take the number 31,223,045 and divide it by 2:

31,223,045 ÷ 2 = 15,611,522.5

If the quotient is a whole number, then 2 and 15,611,522.5 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 31,223,045
-1 -31,223,045

Now, we try dividing 31,223,045 by 3:

31,223,045 ÷ 3 = 10,407,681.6667

If the quotient is a whole number, then 3 and 10,407,681.6667 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 31,223,045
-1 -31,223,045

Let's try dividing by 4:

31,223,045 ÷ 4 = 7,805,761.25

If the quotient is a whole number, then 4 and 7,805,761.25 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 31,223,045
-1 31,223,045
Keep dividing by the next highest number until you cannot divide anymore.

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

1573135491552172451,0851,5194,1117,59520,55528,777127,441143,885201,439637,205892,0871,007,1954,460,4356,244,60931,223,045
-1-5-7-31-35-49-155-217-245-1,085-1,519-4,111-7,595-20,555-28,777-127,441-143,885-201,439-637,205-892,087-1,007,195-4,460,435-6,244,609-31,223,045

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