Q: What are the factor combinations of the number 35,200,123?

 A:
Positive:   1 x 352001237 x 502858989 x 395507623 x 56501
Negative: -1 x -35200123-7 x -5028589-89 x -395507-623 x -56501


How do I find the factor combinations of the number 35,200,123?

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 35,200,123, 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 35,200,123
-1 -35,200,123

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 35,200,123.

Example:
1 x 35,200,123 = 35,200,123
and
-1 x -35,200,123 = 35,200,123
Notice both answers equal 35,200,123

With that explanation out of the way, let's continue. Next, we take the number 35,200,123 and divide it by 2:

35,200,123 ÷ 2 = 17,600,061.5

If the quotient is a whole number, then 2 and 17,600,061.5 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 35,200,123
-1 -35,200,123

Now, we try dividing 35,200,123 by 3:

35,200,123 ÷ 3 = 11,733,374.3333

If the quotient is a whole number, then 3 and 11,733,374.3333 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 35,200,123
-1 -35,200,123

Let's try dividing by 4:

35,200,123 ÷ 4 = 8,800,030.75

If the quotient is a whole number, then 4 and 8,800,030.75 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 35,200,123
-1 35,200,123
Keep dividing by the next highest number until you cannot divide anymore.

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

178962356,501395,5075,028,58935,200,123
-1-7-89-623-56,501-395,507-5,028,589-35,200,123

More Examples

Here are some more numbers to try:

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