Q: What are the factor combinations of the number 221,233,529?

 A:
Positive:   1 x 22123352911 x 2011213917 x 13013737187 x 1183067277 x 7986773047 x 726074271 x 517994709 x 46981
Negative: -1 x -221233529-11 x -20112139-17 x -13013737-187 x -1183067-277 x -798677-3047 x -72607-4271 x -51799-4709 x -46981


How do I find the factor combinations of the number 221,233,529?

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 221,233,529, 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.

1 221,233,529
-1 -221,233,529

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 221,233,529.

Example:
1 x 221,233,529 = 221,233,529
and
-1 x -221,233,529 = 221,233,529
Notice both answers equal 221,233,529

With that explanation out of the way, let's continue. Next, we take the number 221,233,529 and divide it by 2:

221,233,529 ÷ 2 = 110,616,764.5

If the quotient is a whole number, then 2 and 110,616,764.5 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:

1 221,233,529
-1 -221,233,529

Now, we try dividing 221,233,529 by 3:

221,233,529 ÷ 3 = 73,744,509.6667

If the quotient is a whole number, then 3 and 73,744,509.6667 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:

1 221,233,529
-1 -221,233,529

Let's try dividing by 4:

221,233,529 ÷ 4 = 55,308,382.25

If the quotient is a whole number, then 4 and 55,308,382.25 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:

1 221,233,529
-1 221,233,529
Keep dividing by the next highest number until you cannot divide anymore.

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

111171872773,0474,2714,70946,98151,79972,607798,6771,183,06713,013,73720,112,139221,233,529
-1-11-17-187-277-3,047-4,271-4,709-46,981-51,799-72,607-798,677-1,183,067-13,013,737-20,112,139-221,233,529

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