Q: What are the factor combinations of the number 10,820,705?

 A:
Positive:   1 x 108207055 x 21641417 x 154581531 x 34905535 x 309163155 x 69811217 x 498651085 x 9973
Negative: -1 x -10820705-5 x -2164141-7 x -1545815-31 x -349055-35 x -309163-155 x -69811-217 x -49865-1085 x -9973


How do I find the factor combinations of the number 10,820,705?

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 10,820,705, 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 10,820,705
-1 -10,820,705

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 10,820,705.

Example:
1 x 10,820,705 = 10,820,705
and
-1 x -10,820,705 = 10,820,705
Notice both answers equal 10,820,705

With that explanation out of the way, let's continue. Next, we take the number 10,820,705 and divide it by 2:

10,820,705 ÷ 2 = 5,410,352.5

If the quotient is a whole number, then 2 and 5,410,352.5 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 10,820,705
-1 -10,820,705

Now, we try dividing 10,820,705 by 3:

10,820,705 ÷ 3 = 3,606,901.6667

If the quotient is a whole number, then 3 and 3,606,901.6667 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 10,820,705
-1 -10,820,705

Let's try dividing by 4:

10,820,705 ÷ 4 = 2,705,176.25

If the quotient is a whole number, then 4 and 2,705,176.25 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 10,820,705
-1 10,820,705
Keep dividing by the next highest number until you cannot divide anymore.

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

15731351552171,0859,97349,86569,811309,163349,0551,545,8152,164,14110,820,705
-1-5-7-31-35-155-217-1,085-9,973-49,865-69,811-309,163-349,055-1,545,815-2,164,141-10,820,705

More Examples

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