Q: What are the factor combinations of the number 727,125,012?

 A:
Positive:   1 x 7271250122 x 3635625063 x 2423750044 x 1817812536 x 1211875029 x 8079166812 x 6059375118 x 4039583427 x 2693055636 x 2019791743 x 1690988454 x 1346527881 x 897685286 x 8454942108 x 6732639129 x 5636628162 x 4488426172 x 4227471243 x 2992284258 x 2818314324 x 2244213387 x 1878876486 x 1496142516 x 1409157729 x 997428774 x 939438972 x 7480711161 x 6262921458 x 4987141548 x 4697191933 x 3761642187 x 3324762322 x 3131462916 x 2493573483 x 2087643866 x 1880824374 x 1662384644 x 1565735799 x 1253886966 x 1043827732 x 940418748 x 8311910449 x 6958811598 x 6269413932 x 5219117397 x 4179620898 x 3479423196 x 31347
Negative: -1 x -727125012-2 x -363562506-3 x -242375004-4 x -181781253-6 x -121187502-9 x -80791668-12 x -60593751-18 x -40395834-27 x -26930556-36 x -20197917-43 x -16909884-54 x -13465278-81 x -8976852-86 x -8454942-108 x -6732639-129 x -5636628-162 x -4488426-172 x -4227471-243 x -2992284-258 x -2818314-324 x -2244213-387 x -1878876-486 x -1496142-516 x -1409157-729 x -997428-774 x -939438-972 x -748071-1161 x -626292-1458 x -498714-1548 x -469719-1933 x -376164-2187 x -332476-2322 x -313146-2916 x -249357-3483 x -208764-3866 x -188082-4374 x -166238-4644 x -156573-5799 x -125388-6966 x -104382-7732 x -94041-8748 x -83119-10449 x -69588-11598 x -62694-13932 x -52191-17397 x -41796-20898 x -34794-23196 x -31347


How do I find the factor combinations of the number 727,125,012?

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 727,125,012, 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.

1 727,125,012
-1 -727,125,012

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 727,125,012.

Example:
1 x 727,125,012 = 727,125,012
and
-1 x -727,125,012 = 727,125,012
Notice both answers equal 727,125,012

With that explanation out of the way, let's continue. Next, we take the number 727,125,012 and divide it by 2:

727,125,012 ÷ 2 = 363,562,506

If the quotient is a whole number, then 2 and 363,562,506 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 2 363,562,506 727,125,012
-1 -2 -363,562,506 -727,125,012

Now, we try dividing 727,125,012 by 3:

727,125,012 ÷ 3 = 242,375,004

If the quotient is a whole number, then 3 and 242,375,004 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 3 242,375,004 363,562,506 727,125,012
-1 -2 -3 -242,375,004 -363,562,506 -727,125,012

Let's try dividing by 4:

727,125,012 ÷ 4 = 181,781,253

If the quotient is a whole number, then 4 and 181,781,253 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 4 181,781,253 242,375,004 363,562,506 727,125,012
-1 -2 -3 -4 -181,781,253 -242,375,004 -363,562,506 727,125,012
Keep dividing by the next highest number until you cannot divide anymore.

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

12346912182736435481861081291621722432583243874865167297749721,1611,4581,5481,9332,1872,3222,9163,4833,8664,3744,6445,7996,9667,7328,74810,44911,59813,93217,39720,89823,19631,34734,79441,79652,19162,69469,58883,11994,041104,382125,388156,573166,238188,082208,764249,357313,146332,476376,164469,719498,714626,292748,071939,438997,4281,409,1571,496,1421,878,8762,244,2132,818,3142,992,2844,227,4714,488,4265,636,6286,732,6398,454,9428,976,85213,465,27816,909,88420,197,91726,930,55640,395,83460,593,75180,791,668121,187,502181,781,253242,375,004363,562,506727,125,012
-1-2-3-4-6-9-12-18-27-36-43-54-81-86-108-129-162-172-243-258-324-387-486-516-729-774-972-1,161-1,458-1,548-1,933-2,187-2,322-2,916-3,483-3,866-4,374-4,644-5,799-6,966-7,732-8,748-10,449-11,598-13,932-17,397-20,898-23,196-31,347-34,794-41,796-52,191-62,694-69,588-83,119-94,041-104,382-125,388-156,573-166,238-188,082-208,764-249,357-313,146-332,476-376,164-469,719-498,714-626,292-748,071-939,438-997,428-1,409,157-1,496,142-1,878,876-2,244,213-2,818,314-2,992,284-4,227,471-4,488,426-5,636,628-6,732,639-8,454,942-8,976,852-13,465,278-16,909,884-20,197,917-26,930,556-40,395,834-60,593,751-80,791,668-121,187,502-181,781,253-242,375,004-363,562,506-727,125,012

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727,125,010727,125,011727,125,013727,125,014
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