Q: What are the factor combinations of the number 10,021,235?

 A:
Positive:   1 x 100212355 x 20042477 x 143160535 x 28632149 x 204515245 x 40903
Negative: -1 x -10021235-5 x -2004247-7 x -1431605-35 x -286321-49 x -204515-245 x -40903


How do I find the factor combinations of the number 10,021,235?

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 10,021,235, 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 10,021,235
-1 -10,021,235

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 10,021,235.

Example:
1 x 10,021,235 = 10,021,235
and
-1 x -10,021,235 = 10,021,235
Notice both answers equal 10,021,235

With that explanation out of the way, let's continue. Next, we take the number 10,021,235 and divide it by 2:

10,021,235 ÷ 2 = 5,010,617.5

If the quotient is a whole number, then 2 and 5,010,617.5 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 10,021,235
-1 -10,021,235

Now, we try dividing 10,021,235 by 3:

10,021,235 ÷ 3 = 3,340,411.6667

If the quotient is a whole number, then 3 and 3,340,411.6667 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 10,021,235
-1 -10,021,235

Let's try dividing by 4:

10,021,235 ÷ 4 = 2,505,308.75

If the quotient is a whole number, then 4 and 2,505,308.75 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 10,021,235
-1 10,021,235
Keep dividing by the next highest number until you cannot divide anymore.

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

157354924540,903204,515286,3211,431,6052,004,24710,021,235
-1-5-7-35-49-245-40,903-204,515-286,321-1,431,605-2,004,247-10,021,235

More Examples

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