Q: What are the factor combinations of the number 304,120,560?

 A:
Positive:   1 x 3041205602 x 1520602803 x 1013735204 x 760301405 x 608241126 x 506867608 x 3801507010 x 3041205612 x 2534338015 x 2027470416 x 1900753520 x 1520602824 x 1267169030 x 1013735240 x 760301448 x 633584560 x 506867680 x 3801507120 x 2534338240 x 1267169977 x 3112801297 x 2344801954 x 1556402594 x 1172402931 x 1037603891 x 781603908 x 778204885 x 622565188 x 586205862 x 518806485 x 468967782 x 390807816 x 389109770 x 3112810376 x 2931011724 x 2594012970 x 2344814655 x 2075215564 x 1954015632 x 19455
Negative: -1 x -304120560-2 x -152060280-3 x -101373520-4 x -76030140-5 x -60824112-6 x -50686760-8 x -38015070-10 x -30412056-12 x -25343380-15 x -20274704-16 x -19007535-20 x -15206028-24 x -12671690-30 x -10137352-40 x -7603014-48 x -6335845-60 x -5068676-80 x -3801507-120 x -2534338-240 x -1267169-977 x -311280-1297 x -234480-1954 x -155640-2594 x -117240-2931 x -103760-3891 x -78160-3908 x -77820-4885 x -62256-5188 x -58620-5862 x -51880-6485 x -46896-7782 x -39080-7816 x -38910-9770 x -31128-10376 x -29310-11724 x -25940-12970 x -23448-14655 x -20752-15564 x -19540-15632 x -19455


How do I find the factor combinations of the number 304,120,560?

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 304,120,560, 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.

1 304,120,560
-1 -304,120,560

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 304,120,560.

Example:
1 x 304,120,560 = 304,120,560
and
-1 x -304,120,560 = 304,120,560
Notice both answers equal 304,120,560

With that explanation out of the way, let's continue. Next, we take the number 304,120,560 and divide it by 2:

304,120,560 ÷ 2 = 152,060,280

If the quotient is a whole number, then 2 and 152,060,280 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 2 152,060,280 304,120,560
-1 -2 -152,060,280 -304,120,560

Now, we try dividing 304,120,560 by 3:

304,120,560 ÷ 3 = 101,373,520

If the quotient is a whole number, then 3 and 101,373,520 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 3 101,373,520 152,060,280 304,120,560
-1 -2 -3 -101,373,520 -152,060,280 -304,120,560

Let's try dividing by 4:

304,120,560 ÷ 4 = 76,030,140

If the quotient is a whole number, then 4 and 76,030,140 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 76,030,140 101,373,520 152,060,280 304,120,560
-1 -2 -3 -4 -76,030,140 -101,373,520 -152,060,280 304,120,560
Keep dividing by the next highest number until you cannot divide anymore.

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

123456810121516202430404860801202409771,2971,9542,5942,9313,8913,9084,8855,1885,8626,4857,7827,8169,77010,37611,72412,97014,65515,56415,63219,45519,54020,75223,44825,94029,31031,12838,91039,08046,89651,88058,62062,25677,82078,160103,760117,240155,640234,480311,2801,267,1692,534,3383,801,5075,068,6766,335,8457,603,01410,137,35212,671,69015,206,02819,007,53520,274,70425,343,38030,412,05638,015,07050,686,76060,824,11276,030,140101,373,520152,060,280304,120,560
-1-2-3-4-5-6-8-10-12-15-16-20-24-30-40-48-60-80-120-240-977-1,297-1,954-2,594-2,931-3,891-3,908-4,885-5,188-5,862-6,485-7,782-7,816-9,770-10,376-11,724-12,970-14,655-15,564-15,632-19,455-19,540-20,752-23,448-25,940-29,310-31,128-38,910-39,080-46,896-51,880-58,620-62,256-77,820-78,160-103,760-117,240-155,640-234,480-311,280-1,267,169-2,534,338-3,801,507-5,068,676-6,335,845-7,603,014-10,137,352-12,671,690-15,206,028-19,007,535-20,274,704-25,343,380-30,412,056-38,015,070-50,686,760-60,824,112-76,030,140-101,373,520-152,060,280-304,120,560

More Examples

Here are some more numbers to try:

304,120,558304,120,559304,120,561304,120,562
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