Q: What are the factor combinations of the number 72,462,072?

 A:
Positive:   1 x 724620722 x 362310363 x 241540244 x 181155186 x 120770128 x 905775912 x 603850624 x 3019253
Negative: -1 x -72462072-2 x -36231036-3 x -24154024-4 x -18115518-6 x -12077012-8 x -9057759-12 x -6038506-24 x -3019253


How do I find the factor combinations of the number 72,462,072?

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 72,462,072, 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 72,462,072
-1 -72,462,072

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 72,462,072.

Example:
1 x 72,462,072 = 72,462,072
and
-1 x -72,462,072 = 72,462,072
Notice both answers equal 72,462,072

With that explanation out of the way, let's continue. Next, we take the number 72,462,072 and divide it by 2:

72,462,072 ÷ 2 = 36,231,036

If the quotient is a whole number, then 2 and 36,231,036 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 36,231,036 72,462,072
-1 -2 -36,231,036 -72,462,072

Now, we try dividing 72,462,072 by 3:

72,462,072 ÷ 3 = 24,154,024

If the quotient is a whole number, then 3 and 24,154,024 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 24,154,024 36,231,036 72,462,072
-1 -2 -3 -24,154,024 -36,231,036 -72,462,072

Let's try dividing by 4:

72,462,072 ÷ 4 = 18,115,518

If the quotient is a whole number, then 4 and 18,115,518 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 18,115,518 24,154,024 36,231,036 72,462,072
-1 -2 -3 -4 -18,115,518 -24,154,024 -36,231,036 72,462,072
Keep dividing by the next highest number until you cannot divide anymore.

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

12346812243,019,2536,038,5069,057,75912,077,01218,115,51824,154,02436,231,03672,462,072
-1-2-3-4-6-8-12-24-3,019,253-6,038,506-9,057,759-12,077,012-18,115,518-24,154,024-36,231,036-72,462,072

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