Q: What are the factor combinations of the number 35,701,529?

 A:
Positive:   1 x 3570152941 x 87076947 x 75960797 x 368057191 x 1869191927 x 185273977 x 89774559 x 7831
Negative: -1 x -35701529-41 x -870769-47 x -759607-97 x -368057-191 x -186919-1927 x -18527-3977 x -8977-4559 x -7831


How do I find the factor combinations of the number 35,701,529?

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 35,701,529, 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 35,701,529
-1 -35,701,529

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 35,701,529.

Example:
1 x 35,701,529 = 35,701,529
and
-1 x -35,701,529 = 35,701,529
Notice both answers equal 35,701,529

With that explanation out of the way, let's continue. Next, we take the number 35,701,529 and divide it by 2:

35,701,529 ÷ 2 = 17,850,764.5

If the quotient is a whole number, then 2 and 17,850,764.5 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 35,701,529
-1 -35,701,529

Now, we try dividing 35,701,529 by 3:

35,701,529 ÷ 3 = 11,900,509.6667

If the quotient is a whole number, then 3 and 11,900,509.6667 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 35,701,529
-1 -35,701,529

Let's try dividing by 4:

35,701,529 ÷ 4 = 8,925,382.25

If the quotient is a whole number, then 4 and 8,925,382.25 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 35,701,529
-1 35,701,529
Keep dividing by the next highest number until you cannot divide anymore.

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

14147971911,9273,9774,5597,8318,97718,527186,919368,057759,607870,76935,701,529
-1-41-47-97-191-1,927-3,977-4,559-7,831-8,977-18,527-186,919-368,057-759,607-870,769-35,701,529

More Examples

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