Q: What are the factor combinations of the number 30,968,616?

 A:
Positive:   1 x 309686162 x 154843083 x 103228724 x 77421546 x 51614367 x 44240888 x 387107712 x 258071814 x 221204421 x 147469624 x 129035928 x 110602242 x 73734856 x 55301184 x 368674168 x 184337
Negative: -1 x -30968616-2 x -15484308-3 x -10322872-4 x -7742154-6 x -5161436-7 x -4424088-8 x -3871077-12 x -2580718-14 x -2212044-21 x -1474696-24 x -1290359-28 x -1106022-42 x -737348-56 x -553011-84 x -368674-168 x -184337


How do I find the factor combinations of the number 30,968,616?

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 30,968,616, 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 30,968,616
-1 -30,968,616

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 30,968,616.

Example:
1 x 30,968,616 = 30,968,616
and
-1 x -30,968,616 = 30,968,616
Notice both answers equal 30,968,616

With that explanation out of the way, let's continue. Next, we take the number 30,968,616 and divide it by 2:

30,968,616 ÷ 2 = 15,484,308

If the quotient is a whole number, then 2 and 15,484,308 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 15,484,308 30,968,616
-1 -2 -15,484,308 -30,968,616

Now, we try dividing 30,968,616 by 3:

30,968,616 ÷ 3 = 10,322,872

If the quotient is a whole number, then 3 and 10,322,872 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 10,322,872 15,484,308 30,968,616
-1 -2 -3 -10,322,872 -15,484,308 -30,968,616

Let's try dividing by 4:

30,968,616 ÷ 4 = 7,742,154

If the quotient is a whole number, then 4 and 7,742,154 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 7,742,154 10,322,872 15,484,308 30,968,616
-1 -2 -3 -4 -7,742,154 -10,322,872 -15,484,308 30,968,616
Keep dividing by the next highest number until you cannot divide anymore.

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

12346781214212428425684168184,337368,674553,011737,3481,106,0221,290,3591,474,6962,212,0442,580,7183,871,0774,424,0885,161,4367,742,15410,322,87215,484,30830,968,616
-1-2-3-4-6-7-8-12-14-21-24-28-42-56-84-168-184,337-368,674-553,011-737,348-1,106,022-1,290,359-1,474,696-2,212,044-2,580,718-3,871,077-4,424,088-5,161,436-7,742,154-10,322,872-15,484,308-30,968,616

More Examples

Here are some more numbers to try:

30,968,61430,968,61530,968,61730,968,618
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