Q: What are the factor combinations of the number 7,743,025?

 A:
Positive:   1 x 77430255 x 154860525 x 30972131 x 24977597 x 79825103 x 75175155 x 49955485 x 15965515 x 15035775 x 99912425 x 31932575 x 3007
Negative: -1 x -7743025-5 x -1548605-25 x -309721-31 x -249775-97 x -79825-103 x -75175-155 x -49955-485 x -15965-515 x -15035-775 x -9991-2425 x -3193-2575 x -3007


How do I find the factor combinations of the number 7,743,025?

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 7,743,025, 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 7,743,025
-1 -7,743,025

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 7,743,025.

Example:
1 x 7,743,025 = 7,743,025
and
-1 x -7,743,025 = 7,743,025
Notice both answers equal 7,743,025

With that explanation out of the way, let's continue. Next, we take the number 7,743,025 and divide it by 2:

7,743,025 ÷ 2 = 3,871,512.5

If the quotient is a whole number, then 2 and 3,871,512.5 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 7,743,025
-1 -7,743,025

Now, we try dividing 7,743,025 by 3:

7,743,025 ÷ 3 = 2,581,008.3333

If the quotient is a whole number, then 3 and 2,581,008.3333 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 7,743,025
-1 -7,743,025

Let's try dividing by 4:

7,743,025 ÷ 4 = 1,935,756.25

If the quotient is a whole number, then 4 and 1,935,756.25 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 7,743,025
-1 7,743,025
Keep dividing by the next highest number until you cannot divide anymore.

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

152531971031554855157752,4252,5753,0073,1939,99115,03515,96549,95575,17579,825249,775309,7211,548,6057,743,025
-1-5-25-31-97-103-155-485-515-775-2,425-2,575-3,007-3,193-9,991-15,035-15,965-49,955-75,175-79,825-249,775-309,721-1,548,605-7,743,025

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