Q: What are the factor combinations of the number 510,314,500?

 A:
Positive:   1 x 5103145002 x 2551572504 x 1275786255 x 10206290010 x 5103145017 x 3001850020 x 2551572525 x 2041258034 x 1500925050 x 1020629068 x 750462585 x 6003700100 x 5103145125 x 4082516170 x 3001850250 x 2041258340 x 1500925425 x 1200740500 x 1020629850 x 6003701700 x 3001852125 x 2401484250 x 1200748500 x 60037
Negative: -1 x -510314500-2 x -255157250-4 x -127578625-5 x -102062900-10 x -51031450-17 x -30018500-20 x -25515725-25 x -20412580-34 x -15009250-50 x -10206290-68 x -7504625-85 x -6003700-100 x -5103145-125 x -4082516-170 x -3001850-250 x -2041258-340 x -1500925-425 x -1200740-500 x -1020629-850 x -600370-1700 x -300185-2125 x -240148-4250 x -120074-8500 x -60037


How do I find the factor combinations of the number 510,314,500?

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 510,314,500, 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.

1 510,314,500
-1 -510,314,500

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 510,314,500.

Example:
1 x 510,314,500 = 510,314,500
and
-1 x -510,314,500 = 510,314,500
Notice both answers equal 510,314,500

With that explanation out of the way, let's continue. Next, we take the number 510,314,500 and divide it by 2:

510,314,500 ÷ 2 = 255,157,250

If the quotient is a whole number, then 2 and 255,157,250 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 2 255,157,250 510,314,500
-1 -2 -255,157,250 -510,314,500

Now, we try dividing 510,314,500 by 3:

510,314,500 ÷ 3 = 170,104,833.3333

If the quotient is a whole number, then 3 and 170,104,833.3333 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 2 255,157,250 510,314,500
-1 -2 -255,157,250 -510,314,500

Let's try dividing by 4:

510,314,500 ÷ 4 = 127,578,625

If the quotient is a whole number, then 4 and 127,578,625 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 4 127,578,625 255,157,250 510,314,500
-1 -2 -4 -127,578,625 -255,157,250 510,314,500
Keep dividing by the next highest number until you cannot divide anymore.

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

124510172025345068851001251702503404255008501,7002,1254,2508,50060,037120,074240,148300,185600,3701,020,6291,200,7401,500,9252,041,2583,001,8504,082,5165,103,1456,003,7007,504,62510,206,29015,009,25020,412,58025,515,72530,018,50051,031,450102,062,900127,578,625255,157,250510,314,500
-1-2-4-5-10-17-20-25-34-50-68-85-100-125-170-250-340-425-500-850-1,700-2,125-4,250-8,500-60,037-120,074-240,148-300,185-600,370-1,020,629-1,200,740-1,500,925-2,041,258-3,001,850-4,082,516-5,103,145-6,003,700-7,504,625-10,206,290-15,009,250-20,412,580-25,515,725-30,018,500-51,031,450-102,062,900-127,578,625-255,157,250-510,314,500

More Examples

Here are some more numbers to try:

510,314,498510,314,499510,314,501510,314,502
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