Q: What are the factor combinations of the number 431,442,221?

 A:
Positive:   1 x 4314422217 x 6163460331 x 1391749141 x 1052298171 x 6076651217 x 1988213287 x 1503283497 x 868093683 x 6316871271 x 3394512201 x 1960212911 x 1482114781 x 902418897 x 4849315407 x 2800320377 x 21173
Negative: -1 x -431442221-7 x -61634603-31 x -13917491-41 x -10522981-71 x -6076651-217 x -1988213-287 x -1503283-497 x -868093-683 x -631687-1271 x -339451-2201 x -196021-2911 x -148211-4781 x -90241-8897 x -48493-15407 x -28003-20377 x -21173


How do I find the factor combinations of the number 431,442,221?

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 431,442,221, 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.

1 431,442,221
-1 -431,442,221

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 431,442,221.

Example:
1 x 431,442,221 = 431,442,221
and
-1 x -431,442,221 = 431,442,221
Notice both answers equal 431,442,221

With that explanation out of the way, let's continue. Next, we take the number 431,442,221 and divide it by 2:

431,442,221 ÷ 2 = 215,721,110.5

If the quotient is a whole number, then 2 and 215,721,110.5 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:

1 431,442,221
-1 -431,442,221

Now, we try dividing 431,442,221 by 3:

431,442,221 ÷ 3 = 143,814,073.6667

If the quotient is a whole number, then 3 and 143,814,073.6667 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:

1 431,442,221
-1 -431,442,221

Let's try dividing by 4:

431,442,221 ÷ 4 = 107,860,555.25

If the quotient is a whole number, then 4 and 107,860,555.25 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:

1 431,442,221
-1 431,442,221
Keep dividing by the next highest number until you cannot divide anymore.

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

173141712172874976831,2712,2012,9114,7818,89715,40720,37721,17328,00348,49390,241148,211196,021339,451631,687868,0931,503,2831,988,2136,076,65110,522,98113,917,49161,634,603431,442,221
-1-7-31-41-71-217-287-497-683-1,271-2,201-2,911-4,781-8,897-15,407-20,377-21,173-28,003-48,493-90,241-148,211-196,021-339,451-631,687-868,093-1,503,283-1,988,213-6,076,651-10,522,981-13,917,491-61,634,603-431,442,221

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