Q: What are the factor combinations of the number 1,010,401?

 A:
Positive:   1 x 10104017 x 14434319 x 5317971 x 14231107 x 9443133 x 7597497 x 2033749 x 1349
Negative: -1 x -1010401-7 x -144343-19 x -53179-71 x -14231-107 x -9443-133 x -7597-497 x -2033-749 x -1349


How do I find the factor combinations of the number 1,010,401?

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 1,010,401, 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 1,010,401
-1 -1,010,401

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 1,010,401.

Example:
1 x 1,010,401 = 1,010,401
and
-1 x -1,010,401 = 1,010,401
Notice both answers equal 1,010,401

With that explanation out of the way, let's continue. Next, we take the number 1,010,401 and divide it by 2:

1,010,401 ÷ 2 = 505,200.5

If the quotient is a whole number, then 2 and 505,200.5 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 1,010,401
-1 -1,010,401

Now, we try dividing 1,010,401 by 3:

1,010,401 ÷ 3 = 336,800.3333

If the quotient is a whole number, then 3 and 336,800.3333 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 1,010,401
-1 -1,010,401

Let's try dividing by 4:

1,010,401 ÷ 4 = 252,600.25

If the quotient is a whole number, then 4 and 252,600.25 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 1,010,401
-1 1,010,401
Keep dividing by the next highest number until you cannot divide anymore.

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

1719711071334977491,3492,0337,5979,44314,23153,179144,3431,010,401
-1-7-19-71-107-133-497-749-1,349-2,033-7,597-9,443-14,231-53,179-144,343-1,010,401

More Examples

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