Q: What are the factor combinations of the number 35,229,643?

 A:
Positive:   1 x 35229643107 x 329249337 x 104539977 x 36059
Negative: -1 x -35229643-107 x -329249-337 x -104539-977 x -36059


How do I find the factor combinations of the number 35,229,643?

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 35,229,643, 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 35,229,643
-1 -35,229,643

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 35,229,643.

Example:
1 x 35,229,643 = 35,229,643
and
-1 x -35,229,643 = 35,229,643
Notice both answers equal 35,229,643

With that explanation out of the way, let's continue. Next, we take the number 35,229,643 and divide it by 2:

35,229,643 ÷ 2 = 17,614,821.5

If the quotient is a whole number, then 2 and 17,614,821.5 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 35,229,643
-1 -35,229,643

Now, we try dividing 35,229,643 by 3:

35,229,643 ÷ 3 = 11,743,214.3333

If the quotient is a whole number, then 3 and 11,743,214.3333 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 35,229,643
-1 -35,229,643

Let's try dividing by 4:

35,229,643 ÷ 4 = 8,807,410.75

If the quotient is a whole number, then 4 and 8,807,410.75 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 35,229,643
-1 35,229,643
Keep dividing by the next highest number until you cannot divide anymore.

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

110733797736,059104,539329,24935,229,643
-1-107-337-977-36,059-104,539-329,249-35,229,643

More Examples

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