Q: What are the factor combinations of the number 31,121,440?

 A:
Positive:   1 x 311214402 x 155607204 x 77803605 x 62242887 x 44459208 x 389018010 x 311214414 x 222296016 x 194509020 x 155607228 x 111148032 x 97254535 x 88918437 x 84112040 x 77803656 x 55574070 x 44459274 x 42056080 x 389018112 x 277870140 x 222296148 x 210280160 x 194509185 x 168224224 x 138935259 x 120160280 x 111148296 x 105140370 x 84112518 x 60080560 x 55574592 x 52570740 x 42056751 x 414401036 x 300401120 x 277871184 x 262851295 x 240321480 x 210281502 x 207202072 x 150202590 x 120162960 x 105143004 x 103603755 x 82884144 x 75105180 x 60085257 x 5920
Negative: -1 x -31121440-2 x -15560720-4 x -7780360-5 x -6224288-7 x -4445920-8 x -3890180-10 x -3112144-14 x -2222960-16 x -1945090-20 x -1556072-28 x -1111480-32 x -972545-35 x -889184-37 x -841120-40 x -778036-56 x -555740-70 x -444592-74 x -420560-80 x -389018-112 x -277870-140 x -222296-148 x -210280-160 x -194509-185 x -168224-224 x -138935-259 x -120160-280 x -111148-296 x -105140-370 x -84112-518 x -60080-560 x -55574-592 x -52570-740 x -42056-751 x -41440-1036 x -30040-1120 x -27787-1184 x -26285-1295 x -24032-1480 x -21028-1502 x -20720-2072 x -15020-2590 x -12016-2960 x -10514-3004 x -10360-3755 x -8288-4144 x -7510-5180 x -6008-5257 x -5920


How do I find the factor combinations of the number 31,121,440?

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 31,121,440, 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 31,121,440
-1 -31,121,440

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 31,121,440.

Example:
1 x 31,121,440 = 31,121,440
and
-1 x -31,121,440 = 31,121,440
Notice both answers equal 31,121,440

With that explanation out of the way, let's continue. Next, we take the number 31,121,440 and divide it by 2:

31,121,440 ÷ 2 = 15,560,720

If the quotient is a whole number, then 2 and 15,560,720 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 15,560,720 31,121,440
-1 -2 -15,560,720 -31,121,440

Now, we try dividing 31,121,440 by 3:

31,121,440 ÷ 3 = 10,373,813.3333

If the quotient is a whole number, then 3 and 10,373,813.3333 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 15,560,720 31,121,440
-1 -2 -15,560,720 -31,121,440

Let's try dividing by 4:

31,121,440 ÷ 4 = 7,780,360

If the quotient is a whole number, then 4 and 7,780,360 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 7,780,360 15,560,720 31,121,440
-1 -2 -4 -7,780,360 -15,560,720 31,121,440
Keep dividing by the next highest number until you cannot divide anymore.

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

124578101416202832353740567074801121401481601852242592802963705185605927407511,0361,1201,1841,2951,4801,5022,0722,5902,9603,0043,7554,1445,1805,2575,9206,0087,5108,28810,36010,51412,01615,02020,72021,02824,03226,28527,78730,04041,44042,05652,57055,57460,08084,112105,140111,148120,160138,935168,224194,509210,280222,296277,870389,018420,560444,592555,740778,036841,120889,184972,5451,111,4801,556,0721,945,0902,222,9603,112,1443,890,1804,445,9206,224,2887,780,36015,560,72031,121,440
-1-2-4-5-7-8-10-14-16-20-28-32-35-37-40-56-70-74-80-112-140-148-160-185-224-259-280-296-370-518-560-592-740-751-1,036-1,120-1,184-1,295-1,480-1,502-2,072-2,590-2,960-3,004-3,755-4,144-5,180-5,257-5,920-6,008-7,510-8,288-10,360-10,514-12,016-15,020-20,720-21,028-24,032-26,285-27,787-30,040-41,440-42,056-52,570-55,574-60,080-84,112-105,140-111,148-120,160-138,935-168,224-194,509-210,280-222,296-277,870-389,018-420,560-444,592-555,740-778,036-841,120-889,184-972,545-1,111,480-1,556,072-1,945,090-2,222,960-3,112,144-3,890,180-4,445,920-6,224,288-7,780,360-15,560,720-31,121,440

More Examples

Here are some more numbers to try:

31,121,43831,121,43931,121,44131,121,442
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