Q: What are the factor combinations of the number 199,999,998?

 A:
Positive:   1 x 1999999982 x 999999993 x 666666666 x 333333339 x 2222222211 x 1818181818 x 1111111122 x 909090933 x 606060666 x 303030373 x 273972699 x 2020202101 x 1980198137 x 1459854146 x 1369863198 x 1010101202 x 990099219 x 913242274 x 729927303 x 660066411 x 486618438 x 456621606 x 330033657 x 304414803 x 249066822 x 243309909 x 2200221111 x 1800181233 x 1622061314 x 1522071507 x 1327141606 x 1245331818 x 1100112222 x 900092409 x 830222466 x 811033014 x 663573333 x 600064521 x 442384818 x 415116666 x 300037227 x 276747373 x 271269042 x 221199999 x 2000210001 x 1999813563 x 1474613837 x 14454
Negative: -1 x -199999998-2 x -99999999-3 x -66666666-6 x -33333333-9 x -22222222-11 x -18181818-18 x -11111111-22 x -9090909-33 x -6060606-66 x -3030303-73 x -2739726-99 x -2020202-101 x -1980198-137 x -1459854-146 x -1369863-198 x -1010101-202 x -990099-219 x -913242-274 x -729927-303 x -660066-411 x -486618-438 x -456621-606 x -330033-657 x -304414-803 x -249066-822 x -243309-909 x -220022-1111 x -180018-1233 x -162206-1314 x -152207-1507 x -132714-1606 x -124533-1818 x -110011-2222 x -90009-2409 x -83022-2466 x -81103-3014 x -66357-3333 x -60006-4521 x -44238-4818 x -41511-6666 x -30003-7227 x -27674-7373 x -27126-9042 x -22119-9999 x -20002-10001 x -19998-13563 x -14746-13837 x -14454


How do I find the factor combinations of the number 199,999,998?

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 199,999,998, 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.

1 199,999,998
-1 -199,999,998

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 199,999,998.

Example:
1 x 199,999,998 = 199,999,998
and
-1 x -199,999,998 = 199,999,998
Notice both answers equal 199,999,998

With that explanation out of the way, let's continue. Next, we take the number 199,999,998 and divide it by 2:

199,999,998 ÷ 2 = 99,999,999

If the quotient is a whole number, then 2 and 99,999,999 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 99,999,999 199,999,998
-1 -2 -99,999,999 -199,999,998

Now, we try dividing 199,999,998 by 3:

199,999,998 ÷ 3 = 66,666,666

If the quotient is a whole number, then 3 and 66,666,666 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 66,666,666 99,999,999 199,999,998
-1 -2 -3 -66,666,666 -99,999,999 -199,999,998

Let's try dividing by 4:

199,999,998 ÷ 4 = 49,999,999.5

If the quotient is a whole number, then 4 and 49,999,999.5 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 3 66,666,666 99,999,999 199,999,998
-1 -2 -3 -66,666,666 -99,999,999 199,999,998
Keep dividing by the next highest number until you cannot divide anymore.

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

12369111822336673991011371461982022192743034114386066578038229091,1111,2331,3141,5071,6061,8182,2222,4092,4663,0143,3334,5214,8186,6667,2277,3739,0429,99910,00113,56313,83714,45414,74619,99820,00222,11927,12627,67430,00341,51144,23860,00666,35781,10383,02290,009110,011124,533132,714152,207162,206180,018220,022243,309249,066304,414330,033456,621486,618660,066729,927913,242990,0991,010,1011,369,8631,459,8541,980,1982,020,2022,739,7263,030,3036,060,6069,090,90911,111,11118,181,81822,222,22233,333,33366,666,66699,999,999199,999,998
-1-2-3-6-9-11-18-22-33-66-73-99-101-137-146-198-202-219-274-303-411-438-606-657-803-822-909-1,111-1,233-1,314-1,507-1,606-1,818-2,222-2,409-2,466-3,014-3,333-4,521-4,818-6,666-7,227-7,373-9,042-9,999-10,001-13,563-13,837-14,454-14,746-19,998-20,002-22,119-27,126-27,674-30,003-41,511-44,238-60,006-66,357-81,103-83,022-90,009-110,011-124,533-132,714-152,207-162,206-180,018-220,022-243,309-249,066-304,414-330,033-456,621-486,618-660,066-729,927-913,242-990,099-1,010,101-1,369,863-1,459,854-1,980,198-2,020,202-2,739,726-3,030,303-6,060,606-9,090,909-11,111,111-18,181,818-22,222,222-33,333,333-66,666,666-99,999,999-199,999,998

More Examples

Here are some more numbers to try:

199,999,996199,999,997199,999,999200,000,000
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