Q: What are the factor combinations of the number 138,029,940?

 A:
Positive:   1 x 1380299402 x 690149703 x 460099804 x 345074855 x 276059886 x 230049909 x 1533666010 x 1380299412 x 1150249515 x 920199618 x 766833020 x 690149727 x 511222030 x 460099836 x 383416545 x 306733254 x 255611060 x 230049990 x 1533666108 x 1278055135 x 1022444180 x 766833270 x 511222443 x 311580540 x 255611577 x 239220886 x 1557901154 x 1196101329 x 1038601731 x 797401772 x 778952215 x 623162308 x 598052658 x 519302885 x 478443462 x 398703987 x 346204430 x 311585193 x 265805316 x 259655770 x 239226645 x 207726924 x 199357974 x 173108655 x 159488860 x 1557910386 x 1329011540 x 11961
Negative: -1 x -138029940-2 x -69014970-3 x -46009980-4 x -34507485-5 x -27605988-6 x -23004990-9 x -15336660-10 x -13802994-12 x -11502495-15 x -9201996-18 x -7668330-20 x -6901497-27 x -5112220-30 x -4600998-36 x -3834165-45 x -3067332-54 x -2556110-60 x -2300499-90 x -1533666-108 x -1278055-135 x -1022444-180 x -766833-270 x -511222-443 x -311580-540 x -255611-577 x -239220-886 x -155790-1154 x -119610-1329 x -103860-1731 x -79740-1772 x -77895-2215 x -62316-2308 x -59805-2658 x -51930-2885 x -47844-3462 x -39870-3987 x -34620-4430 x -31158-5193 x -26580-5316 x -25965-5770 x -23922-6645 x -20772-6924 x -19935-7974 x -17310-8655 x -15948-8860 x -15579-10386 x -13290-11540 x -11961


How do I find the factor combinations of the number 138,029,940?

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 138,029,940, 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.

1 138,029,940
-1 -138,029,940

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 138,029,940.

Example:
1 x 138,029,940 = 138,029,940
and
-1 x -138,029,940 = 138,029,940
Notice both answers equal 138,029,940

With that explanation out of the way, let's continue. Next, we take the number 138,029,940 and divide it by 2:

138,029,940 ÷ 2 = 69,014,970

If the quotient is a whole number, then 2 and 69,014,970 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 69,014,970 138,029,940
-1 -2 -69,014,970 -138,029,940

Now, we try dividing 138,029,940 by 3:

138,029,940 ÷ 3 = 46,009,980

If the quotient is a whole number, then 3 and 46,009,980 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 46,009,980 69,014,970 138,029,940
-1 -2 -3 -46,009,980 -69,014,970 -138,029,940

Let's try dividing by 4:

138,029,940 ÷ 4 = 34,507,485

If the quotient is a whole number, then 4 and 34,507,485 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 34,507,485 46,009,980 69,014,970 138,029,940
-1 -2 -3 -4 -34,507,485 -46,009,980 -69,014,970 138,029,940
Keep dividing by the next highest number until you cannot divide anymore.

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

12345691012151820273036455460901081351802704435405778861,1541,3291,7311,7722,2152,3082,6582,8853,4623,9874,4305,1935,3165,7706,6456,9247,9748,6558,86010,38611,54011,96113,29015,57915,94817,31019,93520,77223,92225,96526,58031,15834,62039,87047,84451,93059,80562,31677,89579,740103,860119,610155,790239,220255,611311,580511,222766,8331,022,4441,278,0551,533,6662,300,4992,556,1103,067,3323,834,1654,600,9985,112,2206,901,4977,668,3309,201,99611,502,49513,802,99415,336,66023,004,99027,605,98834,507,48546,009,98069,014,970138,029,940
-1-2-3-4-5-6-9-10-12-15-18-20-27-30-36-45-54-60-90-108-135-180-270-443-540-577-886-1,154-1,329-1,731-1,772-2,215-2,308-2,658-2,885-3,462-3,987-4,430-5,193-5,316-5,770-6,645-6,924-7,974-8,655-8,860-10,386-11,540-11,961-13,290-15,579-15,948-17,310-19,935-20,772-23,922-25,965-26,580-31,158-34,620-39,870-47,844-51,930-59,805-62,316-77,895-79,740-103,860-119,610-155,790-239,220-255,611-311,580-511,222-766,833-1,022,444-1,278,055-1,533,666-2,300,499-2,556,110-3,067,332-3,834,165-4,600,998-5,112,220-6,901,497-7,668,330-9,201,996-11,502,495-13,802,994-15,336,660-23,004,990-27,605,988-34,507,485-46,009,980-69,014,970-138,029,940

More Examples

Here are some more numbers to try:

138,029,938138,029,939138,029,941138,029,942
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