Q: What are the factor combinations of the number 9,301,733?

 A:
Positive:   1 x 93017337 x 132881973 x 127421109 x 85337167 x 55699511 x 18203763 x 121911169 x 7957
Negative: -1 x -9301733-7 x -1328819-73 x -127421-109 x -85337-167 x -55699-511 x -18203-763 x -12191-1169 x -7957


How do I find the factor combinations of the number 9,301,733?

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 9,301,733, 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 9,301,733
-1 -9,301,733

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 9,301,733.

Example:
1 x 9,301,733 = 9,301,733
and
-1 x -9,301,733 = 9,301,733
Notice both answers equal 9,301,733

With that explanation out of the way, let's continue. Next, we take the number 9,301,733 and divide it by 2:

9,301,733 ÷ 2 = 4,650,866.5

If the quotient is a whole number, then 2 and 4,650,866.5 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 9,301,733
-1 -9,301,733

Now, we try dividing 9,301,733 by 3:

9,301,733 ÷ 3 = 3,100,577.6667

If the quotient is a whole number, then 3 and 3,100,577.6667 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 9,301,733
-1 -9,301,733

Let's try dividing by 4:

9,301,733 ÷ 4 = 2,325,433.25

If the quotient is a whole number, then 4 and 2,325,433.25 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 9,301,733
-1 9,301,733
Keep dividing by the next highest number until you cannot divide anymore.

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

17731091675117631,1697,95712,19118,20355,69985,337127,4211,328,8199,301,733
-1-7-73-109-167-511-763-1,169-7,957-12,191-18,203-55,699-85,337-127,421-1,328,819-9,301,733

More Examples

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