Q: What are the factor combinations of the number 74,083,025?

 A:
Positive:   1 x 740830255 x 1481660517 x 435782525 x 296332131 x 238977585 x 871565155 x 477955425 x 174313527 x 140575775 x 955912635 x 281155623 x 13175
Negative: -1 x -74083025-5 x -14816605-17 x -4357825-25 x -2963321-31 x -2389775-85 x -871565-155 x -477955-425 x -174313-527 x -140575-775 x -95591-2635 x -28115-5623 x -13175


How do I find the factor combinations of the number 74,083,025?

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 74,083,025, 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 74,083,025
-1 -74,083,025

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 74,083,025.

Example:
1 x 74,083,025 = 74,083,025
and
-1 x -74,083,025 = 74,083,025
Notice both answers equal 74,083,025

With that explanation out of the way, let's continue. Next, we take the number 74,083,025 and divide it by 2:

74,083,025 ÷ 2 = 37,041,512.5

If the quotient is a whole number, then 2 and 37,041,512.5 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 74,083,025
-1 -74,083,025

Now, we try dividing 74,083,025 by 3:

74,083,025 ÷ 3 = 24,694,341.6667

If the quotient is a whole number, then 3 and 24,694,341.6667 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 74,083,025
-1 -74,083,025

Let's try dividing by 4:

74,083,025 ÷ 4 = 18,520,756.25

If the quotient is a whole number, then 4 and 18,520,756.25 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 74,083,025
-1 74,083,025
Keep dividing by the next highest number until you cannot divide anymore.

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

15172531851554255277752,6355,62313,17528,11595,591140,575174,313477,955871,5652,389,7752,963,3214,357,82514,816,60574,083,025
-1-5-17-25-31-85-155-425-527-775-2,635-5,623-13,175-28,115-95,591-140,575-174,313-477,955-871,565-2,389,775-2,963,321-4,357,825-14,816,605-74,083,025

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