Q: What are the factor combinations of the number 307,500?

 A:
Positive:   1 x 3075002 x 1537503 x 1025004 x 768755 x 615006 x 5125010 x 3075012 x 2562515 x 2050020 x 1537525 x 1230030 x 1025041 x 750050 x 615060 x 512575 x 410082 x 3750100 x 3075123 x 2500125 x 2460150 x 2050164 x 1875205 x 1500246 x 1250250 x 1230300 x 1025375 x 820410 x 750492 x 625500 x 615
Negative: -1 x -307500-2 x -153750-3 x -102500-4 x -76875-5 x -61500-6 x -51250-10 x -30750-12 x -25625-15 x -20500-20 x -15375-25 x -12300-30 x -10250-41 x -7500-50 x -6150-60 x -5125-75 x -4100-82 x -3750-100 x -3075-123 x -2500-125 x -2460-150 x -2050-164 x -1875-205 x -1500-246 x -1250-250 x -1230-300 x -1025-375 x -820-410 x -750-492 x -625-500 x -615


How do I find the factor combinations of the number 307,500?

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 307,500, 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.

1 307,500
-1 -307,500

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 307,500.

Example:
1 x 307,500 = 307,500
and
-1 x -307,500 = 307,500
Notice both answers equal 307,500

With that explanation out of the way, let's continue. Next, we take the number 307,500 and divide it by 2:

307,500 ÷ 2 = 153,750

If the quotient is a whole number, then 2 and 153,750 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 2 153,750 307,500
-1 -2 -153,750 -307,500

Now, we try dividing 307,500 by 3:

307,500 ÷ 3 = 102,500

If the quotient is a whole number, then 3 and 102,500 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 3 102,500 153,750 307,500
-1 -2 -3 -102,500 -153,750 -307,500

Let's try dividing by 4:

307,500 ÷ 4 = 76,875

If the quotient is a whole number, then 4 and 76,875 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 76,875 102,500 153,750 307,500
-1 -2 -3 -4 -76,875 -102,500 -153,750 307,500
Keep dividing by the next highest number until you cannot divide anymore.

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

12345610121520253041506075821001231251501642052462503003754104925006156257508201,0251,2301,2501,5001,8752,0502,4602,5003,0753,7504,1005,1256,1507,50010,25012,30015,37520,50025,62530,75051,25061,50076,875102,500153,750307,500
-1-2-3-4-5-6-10-12-15-20-25-30-41-50-60-75-82-100-123-125-150-164-205-246-250-300-375-410-492-500-615-625-750-820-1,025-1,230-1,250-1,500-1,875-2,050-2,460-2,500-3,075-3,750-4,100-5,125-6,150-7,500-10,250-12,300-15,375-20,500-25,625-30,750-51,250-61,500-76,875-102,500-153,750-307,500

More Examples

Here are some more numbers to try:

307,498307,499307,501307,502
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