Q: What are the factor combinations of the number 739,025?

 A:
Positive:   1 x 7390255 x 1478057 x 10557525 x 2956135 x 2111541 x 18025103 x 7175175 x 4223205 x 3605287 x 2575515 x 1435721 x 1025
Negative: -1 x -739025-5 x -147805-7 x -105575-25 x -29561-35 x -21115-41 x -18025-103 x -7175-175 x -4223-205 x -3605-287 x -2575-515 x -1435-721 x -1025


How do I find the factor combinations of the number 739,025?

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 739,025, 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.

1 739,025
-1 -739,025

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 739,025.

Example:
1 x 739,025 = 739,025
and
-1 x -739,025 = 739,025
Notice both answers equal 739,025

With that explanation out of the way, let's continue. Next, we take the number 739,025 and divide it by 2:

739,025 ÷ 2 = 369,512.5

If the quotient is a whole number, then 2 and 369,512.5 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:

1 739,025
-1 -739,025

Now, we try dividing 739,025 by 3:

739,025 ÷ 3 = 246,341.6667

If the quotient is a whole number, then 3 and 246,341.6667 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:

1 739,025
-1 -739,025

Let's try dividing by 4:

739,025 ÷ 4 = 184,756.25

If the quotient is a whole number, then 4 and 184,756.25 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:

1 739,025
-1 739,025
Keep dividing by the next highest number until you cannot divide anymore.

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

1572535411031752052875157211,0251,4352,5753,6054,2237,17518,02521,11529,561105,575147,805739,025
-1-5-7-25-35-41-103-175-205-287-515-721-1,025-1,435-2,575-3,605-4,223-7,175-18,025-21,115-29,561-105,575-147,805-739,025

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