Q: What are the factor combinations of the number 72,162,643?

 A:
Positive:   1 x 721626437 x 1030894929 x 248836743 x 167820149 x 1472707203 x 355481301 x 2397431181 x 611031247 x 578691421 x 507832107 x 342498267 x 8729
Negative: -1 x -72162643-7 x -10308949-29 x -2488367-43 x -1678201-49 x -1472707-203 x -355481-301 x -239743-1181 x -61103-1247 x -57869-1421 x -50783-2107 x -34249-8267 x -8729


How do I find the factor combinations of the number 72,162,643?

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 72,162,643, 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 72,162,643
-1 -72,162,643

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 72,162,643.

Example:
1 x 72,162,643 = 72,162,643
and
-1 x -72,162,643 = 72,162,643
Notice both answers equal 72,162,643

With that explanation out of the way, let's continue. Next, we take the number 72,162,643 and divide it by 2:

72,162,643 ÷ 2 = 36,081,321.5

If the quotient is a whole number, then 2 and 36,081,321.5 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 72,162,643
-1 -72,162,643

Now, we try dividing 72,162,643 by 3:

72,162,643 ÷ 3 = 24,054,214.3333

If the quotient is a whole number, then 3 and 24,054,214.3333 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 72,162,643
-1 -72,162,643

Let's try dividing by 4:

72,162,643 ÷ 4 = 18,040,660.75

If the quotient is a whole number, then 4 and 18,040,660.75 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 72,162,643
-1 72,162,643
Keep dividing by the next highest number until you cannot divide anymore.

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

172943492033011,1811,2471,4212,1078,2678,72934,24950,78357,86961,103239,743355,4811,472,7071,678,2012,488,36710,308,94972,162,643
-1-7-29-43-49-203-301-1,181-1,247-1,421-2,107-8,267-8,729-34,249-50,783-57,869-61,103-239,743-355,481-1,472,707-1,678,201-2,488,367-10,308,949-72,162,643

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