Q: What are the factor combinations of the number 35,531,125?

 A:
Positive:   1 x 355311255 x 71062257 x 507587525 x 142124535 x 101517549 x 725125125 x 284249175 x 203035245 x 145025875 x 406071225 x 290055801 x 6125
Negative: -1 x -35531125-5 x -7106225-7 x -5075875-25 x -1421245-35 x -1015175-49 x -725125-125 x -284249-175 x -203035-245 x -145025-875 x -40607-1225 x -29005-5801 x -6125


How do I find the factor combinations of the number 35,531,125?

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 35,531,125, 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 35,531,125
-1 -35,531,125

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 35,531,125.

Example:
1 x 35,531,125 = 35,531,125
and
-1 x -35,531,125 = 35,531,125
Notice both answers equal 35,531,125

With that explanation out of the way, let's continue. Next, we take the number 35,531,125 and divide it by 2:

35,531,125 ÷ 2 = 17,765,562.5

If the quotient is a whole number, then 2 and 17,765,562.5 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 35,531,125
-1 -35,531,125

Now, we try dividing 35,531,125 by 3:

35,531,125 ÷ 3 = 11,843,708.3333

If the quotient is a whole number, then 3 and 11,843,708.3333 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 35,531,125
-1 -35,531,125

Let's try dividing by 4:

35,531,125 ÷ 4 = 8,882,781.25

If the quotient is a whole number, then 4 and 8,882,781.25 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 35,531,125
-1 35,531,125
Keep dividing by the next highest number until you cannot divide anymore.

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

1572535491251752458751,2255,8016,12529,00540,607145,025203,035284,249725,1251,015,1751,421,2455,075,8757,106,22535,531,125
-1-5-7-25-35-49-125-175-245-875-1,225-5,801-6,125-29,005-40,607-145,025-203,035-284,249-725,125-1,015,175-1,421,245-5,075,875-7,106,225-35,531,125

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