Q: What are the factor combinations of the number 108,729,144?

 A:
Positive:   1 x 1087291442 x 543645723 x 362430484 x 271822866 x 181215248 x 135911439 x 1208101612 x 906076217 x 639583218 x 604050824 x 453038134 x 319791636 x 302025451 x 213194468 x 159895872 x 1510127102 x 1065972136 x 799479153 x 710648204 x 532986211 x 515304306 x 355324408 x 266493421 x 258264422 x 257652612 x 177662633 x 171768842 x 129132844 x 1288261224 x 888311263 x 860881266 x 858841684 x 645661688 x 644131899 x 572562526 x 430442532 x 429423368 x 322833587 x 303123789 x 286963798 x 286285052 x 215225064 x 214717157 x 151927174 x 151567578 x 143487596 x 1431410104 x 10761
Negative: -1 x -108729144-2 x -54364572-3 x -36243048-4 x -27182286-6 x -18121524-8 x -13591143-9 x -12081016-12 x -9060762-17 x -6395832-18 x -6040508-24 x -4530381-34 x -3197916-36 x -3020254-51 x -2131944-68 x -1598958-72 x -1510127-102 x -1065972-136 x -799479-153 x -710648-204 x -532986-211 x -515304-306 x -355324-408 x -266493-421 x -258264-422 x -257652-612 x -177662-633 x -171768-842 x -129132-844 x -128826-1224 x -88831-1263 x -86088-1266 x -85884-1684 x -64566-1688 x -64413-1899 x -57256-2526 x -43044-2532 x -42942-3368 x -32283-3587 x -30312-3789 x -28696-3798 x -28628-5052 x -21522-5064 x -21471-7157 x -15192-7174 x -15156-7578 x -14348-7596 x -14314-10104 x -10761


How do I find the factor combinations of the number 108,729,144?

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 108,729,144, 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.

1 108,729,144
-1 -108,729,144

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 108,729,144.

Example:
1 x 108,729,144 = 108,729,144
and
-1 x -108,729,144 = 108,729,144
Notice both answers equal 108,729,144

With that explanation out of the way, let's continue. Next, we take the number 108,729,144 and divide it by 2:

108,729,144 ÷ 2 = 54,364,572

If the quotient is a whole number, then 2 and 54,364,572 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 54,364,572 108,729,144
-1 -2 -54,364,572 -108,729,144

Now, we try dividing 108,729,144 by 3:

108,729,144 ÷ 3 = 36,243,048

If the quotient is a whole number, then 3 and 36,243,048 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 36,243,048 54,364,572 108,729,144
-1 -2 -3 -36,243,048 -54,364,572 -108,729,144

Let's try dividing by 4:

108,729,144 ÷ 4 = 27,182,286

If the quotient is a whole number, then 4 and 27,182,286 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 27,182,286 36,243,048 54,364,572 108,729,144
-1 -2 -3 -4 -27,182,286 -36,243,048 -54,364,572 108,729,144
Keep dividing by the next highest number until you cannot divide anymore.

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

12346891217182434365168721021361532042113064084214226126338428441,2241,2631,2661,6841,6881,8992,5262,5323,3683,5873,7893,7985,0525,0647,1577,1747,5787,59610,10410,76114,31414,34815,15615,19221,47121,52228,62828,69630,31232,28342,94243,04457,25664,41364,56685,88486,08888,831128,826129,132171,768177,662257,652258,264266,493355,324515,304532,986710,648799,4791,065,9721,510,1271,598,9582,131,9443,020,2543,197,9164,530,3816,040,5086,395,8329,060,76212,081,01613,591,14318,121,52427,182,28636,243,04854,364,572108,729,144
-1-2-3-4-6-8-9-12-17-18-24-34-36-51-68-72-102-136-153-204-211-306-408-421-422-612-633-842-844-1,224-1,263-1,266-1,684-1,688-1,899-2,526-2,532-3,368-3,587-3,789-3,798-5,052-5,064-7,157-7,174-7,578-7,596-10,104-10,761-14,314-14,348-15,156-15,192-21,471-21,522-28,628-28,696-30,312-32,283-42,942-43,044-57,256-64,413-64,566-85,884-86,088-88,831-128,826-129,132-171,768-177,662-257,652-258,264-266,493-355,324-515,304-532,986-710,648-799,479-1,065,972-1,510,127-1,598,958-2,131,944-3,020,254-3,197,916-4,530,381-6,040,508-6,395,832-9,060,762-12,081,016-13,591,143-18,121,524-27,182,286-36,243,048-54,364,572-108,729,144

More Examples

Here are some more numbers to try:

108,729,142108,729,143108,729,145108,729,146
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