Q: What are the factor combinations of the number 7,504,175?

 A:
Positive:   1 x 75041755 x 15008357 x 107202525 x 30016735 x 214405137 x 54775175 x 42881313 x 23975685 x 10955959 x 78251565 x 47952191 x 3425
Negative: -1 x -7504175-5 x -1500835-7 x -1072025-25 x -300167-35 x -214405-137 x -54775-175 x -42881-313 x -23975-685 x -10955-959 x -7825-1565 x -4795-2191 x -3425


How do I find the factor combinations of the number 7,504,175?

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 7,504,175, 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 7,504,175
-1 -7,504,175

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 7,504,175.

Example:
1 x 7,504,175 = 7,504,175
and
-1 x -7,504,175 = 7,504,175
Notice both answers equal 7,504,175

With that explanation out of the way, let's continue. Next, we take the number 7,504,175 and divide it by 2:

7,504,175 ÷ 2 = 3,752,087.5

If the quotient is a whole number, then 2 and 3,752,087.5 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 7,504,175
-1 -7,504,175

Now, we try dividing 7,504,175 by 3:

7,504,175 ÷ 3 = 2,501,391.6667

If the quotient is a whole number, then 3 and 2,501,391.6667 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 7,504,175
-1 -7,504,175

Let's try dividing by 4:

7,504,175 ÷ 4 = 1,876,043.75

If the quotient is a whole number, then 4 and 1,876,043.75 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 7,504,175
-1 7,504,175
Keep dividing by the next highest number until you cannot divide anymore.

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

15725351371753136859591,5652,1913,4254,7957,82510,95523,97542,88154,775214,405300,1671,072,0251,500,8357,504,175
-1-5-7-25-35-137-175-313-685-959-1,565-2,191-3,425-4,795-7,825-10,955-23,975-42,881-54,775-214,405-300,167-1,072,025-1,500,835-7,504,175

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