Q: What are the factor combinations of the number 10,427,207?

 A:
Positive:   1 x 104272077 x 148960183 x 125629131 x 79597137 x 76111581 x 17947917 x 11371959 x 10873
Negative: -1 x -10427207-7 x -1489601-83 x -125629-131 x -79597-137 x -76111-581 x -17947-917 x -11371-959 x -10873


How do I find the factor combinations of the number 10,427,207?

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 10,427,207, 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 10,427,207
-1 -10,427,207

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 10,427,207.

Example:
1 x 10,427,207 = 10,427,207
and
-1 x -10,427,207 = 10,427,207
Notice both answers equal 10,427,207

With that explanation out of the way, let's continue. Next, we take the number 10,427,207 and divide it by 2:

10,427,207 ÷ 2 = 5,213,603.5

If the quotient is a whole number, then 2 and 5,213,603.5 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 10,427,207
-1 -10,427,207

Now, we try dividing 10,427,207 by 3:

10,427,207 ÷ 3 = 3,475,735.6667

If the quotient is a whole number, then 3 and 3,475,735.6667 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 10,427,207
-1 -10,427,207

Let's try dividing by 4:

10,427,207 ÷ 4 = 2,606,801.75

If the quotient is a whole number, then 4 and 2,606,801.75 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 10,427,207
-1 10,427,207
Keep dividing by the next highest number until you cannot divide anymore.

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

178313113758191795910,87311,37117,94776,11179,597125,6291,489,60110,427,207
-1-7-83-131-137-581-917-959-10,873-11,371-17,947-76,111-79,597-125,629-1,489,601-10,427,207

More Examples

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