Q: What are the factor combinations of the number 657,120,016?

 A:
Positive:   1 x 6571200162 x 3285600084 x 1642800047 x 938742888 x 8214000214 x 4693714416 x 4107000119 x 3458526428 x 2346857238 x 1729263256 x 1173428676 x 8646316109 x 6028624112 x 5867143133 x 4940752152 x 4323158218 x 3014312266 x 2470376304 x 2161579436 x 1507156532 x 1235188763 x 861232872 x 7535781064 x 6175941526 x 4306161744 x 3767892071 x 3172962128 x 3087972833 x 2319523052 x 2153084142 x 1586485666 x 1159766104 x 1076548284 x 7932411332 x 5798812208 x 5382714497 x 4532816568 x 3966219831 x 3313622664 x 28994
Negative: -1 x -657120016-2 x -328560008-4 x -164280004-7 x -93874288-8 x -82140002-14 x -46937144-16 x -41070001-19 x -34585264-28 x -23468572-38 x -17292632-56 x -11734286-76 x -8646316-109 x -6028624-112 x -5867143-133 x -4940752-152 x -4323158-218 x -3014312-266 x -2470376-304 x -2161579-436 x -1507156-532 x -1235188-763 x -861232-872 x -753578-1064 x -617594-1526 x -430616-1744 x -376789-2071 x -317296-2128 x -308797-2833 x -231952-3052 x -215308-4142 x -158648-5666 x -115976-6104 x -107654-8284 x -79324-11332 x -57988-12208 x -53827-14497 x -45328-16568 x -39662-19831 x -33136-22664 x -28994


How do I find the factor combinations of the number 657,120,016?

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 657,120,016, 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.

1 657,120,016
-1 -657,120,016

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 657,120,016.

Example:
1 x 657,120,016 = 657,120,016
and
-1 x -657,120,016 = 657,120,016
Notice both answers equal 657,120,016

With that explanation out of the way, let's continue. Next, we take the number 657,120,016 and divide it by 2:

657,120,016 ÷ 2 = 328,560,008

If the quotient is a whole number, then 2 and 328,560,008 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 2 328,560,008 657,120,016
-1 -2 -328,560,008 -657,120,016

Now, we try dividing 657,120,016 by 3:

657,120,016 ÷ 3 = 219,040,005.3333

If the quotient is a whole number, then 3 and 219,040,005.3333 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 2 328,560,008 657,120,016
-1 -2 -328,560,008 -657,120,016

Let's try dividing by 4:

657,120,016 ÷ 4 = 164,280,004

If the quotient is a whole number, then 4 and 164,280,004 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 4 164,280,004 328,560,008 657,120,016
-1 -2 -4 -164,280,004 -328,560,008 657,120,016
Keep dividing by the next highest number until you cannot divide anymore.

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

12478141619283856761091121331522182663044365327638721,0641,5261,7442,0712,1282,8333,0524,1425,6666,1048,28411,33212,20814,49716,56819,83122,66428,99433,13639,66245,32853,82757,98879,324107,654115,976158,648215,308231,952308,797317,296376,789430,616617,594753,578861,2321,235,1881,507,1562,161,5792,470,3763,014,3124,323,1584,940,7525,867,1436,028,6248,646,31611,734,28617,292,63223,468,57234,585,26441,070,00146,937,14482,140,00293,874,288164,280,004328,560,008657,120,016
-1-2-4-7-8-14-16-19-28-38-56-76-109-112-133-152-218-266-304-436-532-763-872-1,064-1,526-1,744-2,071-2,128-2,833-3,052-4,142-5,666-6,104-8,284-11,332-12,208-14,497-16,568-19,831-22,664-28,994-33,136-39,662-45,328-53,827-57,988-79,324-107,654-115,976-158,648-215,308-231,952-308,797-317,296-376,789-430,616-617,594-753,578-861,232-1,235,188-1,507,156-2,161,579-2,470,376-3,014,312-4,323,158-4,940,752-5,867,143-6,028,624-8,646,316-11,734,286-17,292,632-23,468,572-34,585,264-41,070,001-46,937,144-82,140,002-93,874,288-164,280,004-328,560,008-657,120,016

More Examples

Here are some more numbers to try:

657,120,014657,120,015657,120,017657,120,018
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