Q: What are the factor combinations of the number 73,385?

 A:
Positive:   1 x 733855 x 1467713 x 564565 x 1129
Negative: -1 x -73385-5 x -14677-13 x -5645-65 x -1129


How do I find the factor combinations of the number 73,385?

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 73,385, 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 73,385
-1 -73,385

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 73,385.

Example:
1 x 73,385 = 73,385
and
-1 x -73,385 = 73,385
Notice both answers equal 73,385

With that explanation out of the way, let's continue. Next, we take the number 73,385 and divide it by 2:

73,385 ÷ 2 = 36,692.5

If the quotient is a whole number, then 2 and 36,692.5 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 73,385
-1 -73,385

Now, we try dividing 73,385 by 3:

73,385 ÷ 3 = 24,461.6667

If the quotient is a whole number, then 3 and 24,461.6667 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 73,385
-1 -73,385

Let's try dividing by 4:

73,385 ÷ 4 = 18,346.25

If the quotient is a whole number, then 4 and 18,346.25 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 73,385
-1 73,385
Keep dividing by the next highest number until you cannot divide anymore.

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

1513651,1295,64514,67773,385
-1-5-13-65-1,129-5,645-14,677-73,385

More Examples

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