Q: What are the factor combinations of the number 321,003,424?

 A:
Positive:   1 x 3210034242 x 1605017124 x 802508567 x 458576328 x 4012542814 x 2292881616 x 2006271428 x 1146440832 x 1003135756 x 573220459 x 5440736107 x 3000032112 x 2866102118 x 2720368214 x 1500016224 x 1433051227 x 1414112236 x 1360184413 x 777248428 x 750008454 x 707056472 x 680092749 x 428576826 x 388624856 x 375004908 x 353528944 x 3400461498 x 2142881589 x 2020161652 x 1943121712 x 1875021816 x 1767641888 x 1700232996 x 1071443178 x 1010083304 x 971563424 x 937513632 x 883825992 x 535726313 x 508486356 x 505046608 x 485787264 x 4419111984 x 2678612626 x 2542412712 x 2525213216 x 2428913393 x 23968
Negative: -1 x -321003424-2 x -160501712-4 x -80250856-7 x -45857632-8 x -40125428-14 x -22928816-16 x -20062714-28 x -11464408-32 x -10031357-56 x -5732204-59 x -5440736-107 x -3000032-112 x -2866102-118 x -2720368-214 x -1500016-224 x -1433051-227 x -1414112-236 x -1360184-413 x -777248-428 x -750008-454 x -707056-472 x -680092-749 x -428576-826 x -388624-856 x -375004-908 x -353528-944 x -340046-1498 x -214288-1589 x -202016-1652 x -194312-1712 x -187502-1816 x -176764-1888 x -170023-2996 x -107144-3178 x -101008-3304 x -97156-3424 x -93751-3632 x -88382-5992 x -53572-6313 x -50848-6356 x -50504-6608 x -48578-7264 x -44191-11984 x -26786-12626 x -25424-12712 x -25252-13216 x -24289-13393 x -23968


How do I find the factor combinations of the number 321,003,424?

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 321,003,424, 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.

1 321,003,424
-1 -321,003,424

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 321,003,424.

Example:
1 x 321,003,424 = 321,003,424
and
-1 x -321,003,424 = 321,003,424
Notice both answers equal 321,003,424

With that explanation out of the way, let's continue. Next, we take the number 321,003,424 and divide it by 2:

321,003,424 ÷ 2 = 160,501,712

If the quotient is a whole number, then 2 and 160,501,712 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 2 160,501,712 321,003,424
-1 -2 -160,501,712 -321,003,424

Now, we try dividing 321,003,424 by 3:

321,003,424 ÷ 3 = 107,001,141.3333

If the quotient is a whole number, then 3 and 107,001,141.3333 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 2 160,501,712 321,003,424
-1 -2 -160,501,712 -321,003,424

Let's try dividing by 4:

321,003,424 ÷ 4 = 80,250,856

If the quotient is a whole number, then 4 and 80,250,856 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 4 80,250,856 160,501,712 321,003,424
-1 -2 -4 -80,250,856 -160,501,712 321,003,424
Keep dividing by the next highest number until you cannot divide anymore.

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

124781416283256591071121182142242272364134284544727498268569089441,4981,5891,6521,7121,8161,8882,9963,1783,3043,4243,6325,9926,3136,3566,6087,26411,98412,62612,71213,21613,39323,96824,28925,25225,42426,78644,19148,57850,50450,84853,57288,38293,75197,156101,008107,144170,023176,764187,502194,312202,016214,288340,046353,528375,004388,624428,576680,092707,056750,008777,2481,360,1841,414,1121,433,0511,500,0162,720,3682,866,1023,000,0325,440,7365,732,20410,031,35711,464,40820,062,71422,928,81640,125,42845,857,63280,250,856160,501,712321,003,424
-1-2-4-7-8-14-16-28-32-56-59-107-112-118-214-224-227-236-413-428-454-472-749-826-856-908-944-1,498-1,589-1,652-1,712-1,816-1,888-2,996-3,178-3,304-3,424-3,632-5,992-6,313-6,356-6,608-7,264-11,984-12,626-12,712-13,216-13,393-23,968-24,289-25,252-25,424-26,786-44,191-48,578-50,504-50,848-53,572-88,382-93,751-97,156-101,008-107,144-170,023-176,764-187,502-194,312-202,016-214,288-340,046-353,528-375,004-388,624-428,576-680,092-707,056-750,008-777,248-1,360,184-1,414,112-1,433,051-1,500,016-2,720,368-2,866,102-3,000,032-5,440,736-5,732,204-10,031,357-11,464,408-20,062,714-22,928,816-40,125,428-45,857,632-80,250,856-160,501,712-321,003,424

More Examples

Here are some more numbers to try:

321,003,422321,003,423321,003,425321,003,426
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