Q: What are the factor combinations of the number 10,010,645?

 A:
Positive:   1 x 100106455 x 200212971 x 140995163 x 61415173 x 57865355 x 28199815 x 12283865 x 11573
Negative: -1 x -10010645-5 x -2002129-71 x -140995-163 x -61415-173 x -57865-355 x -28199-815 x -12283-865 x -11573


How do I find the factor combinations of the number 10,010,645?

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 10,010,645, 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 10,010,645
-1 -10,010,645

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 10,010,645.

Example:
1 x 10,010,645 = 10,010,645
and
-1 x -10,010,645 = 10,010,645
Notice both answers equal 10,010,645

With that explanation out of the way, let's continue. Next, we take the number 10,010,645 and divide it by 2:

10,010,645 ÷ 2 = 5,005,322.5

If the quotient is a whole number, then 2 and 5,005,322.5 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 10,010,645
-1 -10,010,645

Now, we try dividing 10,010,645 by 3:

10,010,645 ÷ 3 = 3,336,881.6667

If the quotient is a whole number, then 3 and 3,336,881.6667 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 10,010,645
-1 -10,010,645

Let's try dividing by 4:

10,010,645 ÷ 4 = 2,502,661.25

If the quotient is a whole number, then 4 and 2,502,661.25 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 10,010,645
-1 10,010,645
Keep dividing by the next highest number until you cannot divide anymore.

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

157116317335581586511,57312,28328,19957,86561,415140,9952,002,12910,010,645
-1-5-71-163-173-355-815-865-11,573-12,283-28,199-57,865-61,415-140,995-2,002,129-10,010,645

More Examples

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