Q: What are the factor combinations of the number 35,735,125?

 A:
Positive:   1 x 357351255 x 714702525 x 1429405125 x 285881263 x 1358751087 x 328751315 x 271755435 x 6575
Negative: -1 x -35735125-5 x -7147025-25 x -1429405-125 x -285881-263 x -135875-1087 x -32875-1315 x -27175-5435 x -6575


How do I find the factor combinations of the number 35,735,125?

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 35,735,125, 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 35,735,125
-1 -35,735,125

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 35,735,125.

Example:
1 x 35,735,125 = 35,735,125
and
-1 x -35,735,125 = 35,735,125
Notice both answers equal 35,735,125

With that explanation out of the way, let's continue. Next, we take the number 35,735,125 and divide it by 2:

35,735,125 ÷ 2 = 17,867,562.5

If the quotient is a whole number, then 2 and 17,867,562.5 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 35,735,125
-1 -35,735,125

Now, we try dividing 35,735,125 by 3:

35,735,125 ÷ 3 = 11,911,708.3333

If the quotient is a whole number, then 3 and 11,911,708.3333 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 35,735,125
-1 -35,735,125

Let's try dividing by 4:

35,735,125 ÷ 4 = 8,933,781.25

If the quotient is a whole number, then 4 and 8,933,781.25 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 35,735,125
-1 35,735,125
Keep dividing by the next highest number until you cannot divide anymore.

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

15251252631,0871,3155,4356,57527,17532,875135,875285,8811,429,4057,147,02535,735,125
-1-5-25-125-263-1,087-1,315-5,435-6,575-27,175-32,875-135,875-285,881-1,429,405-7,147,025-35,735,125

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