Q: What are the factor combinations of the number 7,201,019?

 A:
Positive:   1 x 72010197 x 102871719 x 37900129 x 248311133 x 54143203 x 35473551 x 130691867 x 3857
Negative: -1 x -7201019-7 x -1028717-19 x -379001-29 x -248311-133 x -54143-203 x -35473-551 x -13069-1867 x -3857


How do I find the factor combinations of the number 7,201,019?

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 7,201,019, 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 7,201,019
-1 -7,201,019

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 7,201,019.

Example:
1 x 7,201,019 = 7,201,019
and
-1 x -7,201,019 = 7,201,019
Notice both answers equal 7,201,019

With that explanation out of the way, let's continue. Next, we take the number 7,201,019 and divide it by 2:

7,201,019 ÷ 2 = 3,600,509.5

If the quotient is a whole number, then 2 and 3,600,509.5 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 7,201,019
-1 -7,201,019

Now, we try dividing 7,201,019 by 3:

7,201,019 ÷ 3 = 2,400,339.6667

If the quotient is a whole number, then 3 and 2,400,339.6667 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 7,201,019
-1 -7,201,019

Let's try dividing by 4:

7,201,019 ÷ 4 = 1,800,254.75

If the quotient is a whole number, then 4 and 1,800,254.75 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 7,201,019
-1 7,201,019
Keep dividing by the next highest number until you cannot divide anymore.

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

1719291332035511,8673,85713,06935,47354,143248,311379,0011,028,7177,201,019
-1-7-19-29-133-203-551-1,867-3,857-13,069-35,473-54,143-248,311-379,001-1,028,717-7,201,019

More Examples

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