Q: What are the factor combinations of the number 220,114,321?

 A:
Positive:   1 x 2201143217 x 3144490329 x 759014949 x 4492129191 x 1152431203 x 1084307811 x 2714111337 x 1646331421 x 1549015539 x 397395677 x 387739359 x 23519
Negative: -1 x -220114321-7 x -31444903-29 x -7590149-49 x -4492129-191 x -1152431-203 x -1084307-811 x -271411-1337 x -164633-1421 x -154901-5539 x -39739-5677 x -38773-9359 x -23519


How do I find the factor combinations of the number 220,114,321?

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 220,114,321, 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.

1 220,114,321
-1 -220,114,321

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 220,114,321.

Example:
1 x 220,114,321 = 220,114,321
and
-1 x -220,114,321 = 220,114,321
Notice both answers equal 220,114,321

With that explanation out of the way, let's continue. Next, we take the number 220,114,321 and divide it by 2:

220,114,321 ÷ 2 = 110,057,160.5

If the quotient is a whole number, then 2 and 110,057,160.5 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:

1 220,114,321
-1 -220,114,321

Now, we try dividing 220,114,321 by 3:

220,114,321 ÷ 3 = 73,371,440.3333

If the quotient is a whole number, then 3 and 73,371,440.3333 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:

1 220,114,321
-1 -220,114,321

Let's try dividing by 4:

220,114,321 ÷ 4 = 55,028,580.25

If the quotient is a whole number, then 4 and 55,028,580.25 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:

1 220,114,321
-1 220,114,321
Keep dividing by the next highest number until you cannot divide anymore.

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

1729491912038111,3371,4215,5395,6779,35923,51938,77339,739154,901164,633271,4111,084,3071,152,4314,492,1297,590,14931,444,903220,114,321
-1-7-29-49-191-203-811-1,337-1,421-5,539-5,677-9,359-23,519-38,773-39,739-154,901-164,633-271,411-1,084,307-1,152,431-4,492,129-7,590,149-31,444,903-220,114,321

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