Q: What are the factor combinations of the number 12,535,615?

 A:
Positive:   1 x 125356155 x 2507123101 x 124115103 x 121705241 x 52015505 x 24823515 x 243411205 x 10403
Negative: -1 x -12535615-5 x -2507123-101 x -124115-103 x -121705-241 x -52015-505 x -24823-515 x -24341-1205 x -10403


How do I find the factor combinations of the number 12,535,615?

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 12,535,615, 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 12,535,615
-1 -12,535,615

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 12,535,615.

Example:
1 x 12,535,615 = 12,535,615
and
-1 x -12,535,615 = 12,535,615
Notice both answers equal 12,535,615

With that explanation out of the way, let's continue. Next, we take the number 12,535,615 and divide it by 2:

12,535,615 ÷ 2 = 6,267,807.5

If the quotient is a whole number, then 2 and 6,267,807.5 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 12,535,615
-1 -12,535,615

Now, we try dividing 12,535,615 by 3:

12,535,615 ÷ 3 = 4,178,538.3333

If the quotient is a whole number, then 3 and 4,178,538.3333 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 12,535,615
-1 -12,535,615

Let's try dividing by 4:

12,535,615 ÷ 4 = 3,133,903.75

If the quotient is a whole number, then 4 and 3,133,903.75 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 12,535,615
-1 12,535,615
Keep dividing by the next highest number until you cannot divide anymore.

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

151011032415055151,20510,40324,34124,82352,015121,705124,1152,507,12312,535,615
-1-5-101-103-241-505-515-1,205-10,403-24,341-24,823-52,015-121,705-124,115-2,507,123-12,535,615

More Examples

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