Q: What are the factor combinations of the number 72,154,625?

 A:
Positive:   1 x 721546255 x 1443092525 x 288618537 x 1950125125 x 577237185 x 390025925 x 780054625 x 15601
Negative: -1 x -72154625-5 x -14430925-25 x -2886185-37 x -1950125-125 x -577237-185 x -390025-925 x -78005-4625 x -15601


How do I find the factor combinations of the number 72,154,625?

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 72,154,625, 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 72,154,625
-1 -72,154,625

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 72,154,625.

Example:
1 x 72,154,625 = 72,154,625
and
-1 x -72,154,625 = 72,154,625
Notice both answers equal 72,154,625

With that explanation out of the way, let's continue. Next, we take the number 72,154,625 and divide it by 2:

72,154,625 ÷ 2 = 36,077,312.5

If the quotient is a whole number, then 2 and 36,077,312.5 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 72,154,625
-1 -72,154,625

Now, we try dividing 72,154,625 by 3:

72,154,625 ÷ 3 = 24,051,541.6667

If the quotient is a whole number, then 3 and 24,051,541.6667 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 72,154,625
-1 -72,154,625

Let's try dividing by 4:

72,154,625 ÷ 4 = 18,038,656.25

If the quotient is a whole number, then 4 and 18,038,656.25 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 72,154,625
-1 72,154,625
Keep dividing by the next highest number until you cannot divide anymore.

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

1525371251859254,62515,60178,005390,025577,2371,950,1252,886,18514,430,92572,154,625
-1-5-25-37-125-185-925-4,625-15,601-78,005-390,025-577,237-1,950,125-2,886,185-14,430,925-72,154,625

More Examples

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