Q: What are the factor combinations of the number 72,031,603?

 A:
Positive:   1 x 720316037 x 1029022919 x 3791137133 x 541591379 x 1900571429 x 504072653 x 271517201 x 10003
Negative: -1 x -72031603-7 x -10290229-19 x -3791137-133 x -541591-379 x -190057-1429 x -50407-2653 x -27151-7201 x -10003


How do I find the factor combinations of the number 72,031,603?

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 72,031,603, 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 72,031,603
-1 -72,031,603

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 72,031,603.

Example:
1 x 72,031,603 = 72,031,603
and
-1 x -72,031,603 = 72,031,603
Notice both answers equal 72,031,603

With that explanation out of the way, let's continue. Next, we take the number 72,031,603 and divide it by 2:

72,031,603 ÷ 2 = 36,015,801.5

If the quotient is a whole number, then 2 and 36,015,801.5 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 72,031,603
-1 -72,031,603

Now, we try dividing 72,031,603 by 3:

72,031,603 ÷ 3 = 24,010,534.3333

If the quotient is a whole number, then 3 and 24,010,534.3333 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 72,031,603
-1 -72,031,603

Let's try dividing by 4:

72,031,603 ÷ 4 = 18,007,900.75

If the quotient is a whole number, then 4 and 18,007,900.75 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 72,031,603
-1 72,031,603
Keep dividing by the next highest number until you cannot divide anymore.

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

17191333791,4292,6537,20110,00327,15150,407190,057541,5913,791,13710,290,22972,031,603
-1-7-19-133-379-1,429-2,653-7,201-10,003-27,151-50,407-190,057-541,591-3,791,137-10,290,229-72,031,603

More Examples

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