Q: What are the factor combinations of the number 312,211,008?

 A:
Positive:   1 x 3122110082 x 1561055043 x 1040703364 x 780527526 x 520351688 x 390263769 x 3469011212 x 2601758416 x 1951318818 x 1734505624 x 1300879232 x 975659436 x 867252848 x 650439659 x 529171264 x 487829772 x 433626496 x 3252198118 x 2645856144 x 2168132177 x 1763904192 x 1626099236 x 1322928288 x 1084066354 x 881952472 x 661464531 x 587968576 x 542033708 x 440976944 x 3307321062 x 2939841416 x 2204881888 x 1653662124 x 1469922832 x 1102443776 x 826834248 x 734965664 x 551228496 x 367489187 x 3398411328 x 2756116992 x 18374
Negative: -1 x -312211008-2 x -156105504-3 x -104070336-4 x -78052752-6 x -52035168-8 x -39026376-9 x -34690112-12 x -26017584-16 x -19513188-18 x -17345056-24 x -13008792-32 x -9756594-36 x -8672528-48 x -6504396-59 x -5291712-64 x -4878297-72 x -4336264-96 x -3252198-118 x -2645856-144 x -2168132-177 x -1763904-192 x -1626099-236 x -1322928-288 x -1084066-354 x -881952-472 x -661464-531 x -587968-576 x -542033-708 x -440976-944 x -330732-1062 x -293984-1416 x -220488-1888 x -165366-2124 x -146992-2832 x -110244-3776 x -82683-4248 x -73496-5664 x -55122-8496 x -36748-9187 x -33984-11328 x -27561-16992 x -18374


How do I find the factor combinations of the number 312,211,008?

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 312,211,008, 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.

1 312,211,008
-1 -312,211,008

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 312,211,008.

Example:
1 x 312,211,008 = 312,211,008
and
-1 x -312,211,008 = 312,211,008
Notice both answers equal 312,211,008

With that explanation out of the way, let's continue. Next, we take the number 312,211,008 and divide it by 2:

312,211,008 ÷ 2 = 156,105,504

If the quotient is a whole number, then 2 and 156,105,504 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 2 156,105,504 312,211,008
-1 -2 -156,105,504 -312,211,008

Now, we try dividing 312,211,008 by 3:

312,211,008 ÷ 3 = 104,070,336

If the quotient is a whole number, then 3 and 104,070,336 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 3 104,070,336 156,105,504 312,211,008
-1 -2 -3 -104,070,336 -156,105,504 -312,211,008

Let's try dividing by 4:

312,211,008 ÷ 4 = 78,052,752

If the quotient is a whole number, then 4 and 78,052,752 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 78,052,752 104,070,336 156,105,504 312,211,008
-1 -2 -3 -4 -78,052,752 -104,070,336 -156,105,504 312,211,008
Keep dividing by the next highest number until you cannot divide anymore.

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

123468912161824323648596472961181441771922362883544725315767089441,0621,4161,8882,1242,8323,7764,2485,6648,4969,18711,32816,99218,37427,56133,98436,74855,12273,49682,683110,244146,992165,366220,488293,984330,732440,976542,033587,968661,464881,9521,084,0661,322,9281,626,0991,763,9042,168,1322,645,8563,252,1984,336,2644,878,2975,291,7126,504,3968,672,5289,756,59413,008,79217,345,05619,513,18826,017,58434,690,11239,026,37652,035,16878,052,752104,070,336156,105,504312,211,008
-1-2-3-4-6-8-9-12-16-18-24-32-36-48-59-64-72-96-118-144-177-192-236-288-354-472-531-576-708-944-1,062-1,416-1,888-2,124-2,832-3,776-4,248-5,664-8,496-9,187-11,328-16,992-18,374-27,561-33,984-36,748-55,122-73,496-82,683-110,244-146,992-165,366-220,488-293,984-330,732-440,976-542,033-587,968-661,464-881,952-1,084,066-1,322,928-1,626,099-1,763,904-2,168,132-2,645,856-3,252,198-4,336,264-4,878,297-5,291,712-6,504,396-8,672,528-9,756,594-13,008,792-17,345,056-19,513,188-26,017,584-34,690,112-39,026,376-52,035,168-78,052,752-104,070,336-156,105,504-312,211,008

More Examples

Here are some more numbers to try:

312,211,006312,211,007312,211,009312,211,010
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