Q: What are the factor combinations of the number 101,101,000?

 A:
Positive:   1 x 1011010002 x 505505004 x 252752505 x 202202007 x 144430008 x 1263762510 x 1011010011 x 919100013 x 777700014 x 722150020 x 505505022 x 459550025 x 404404026 x 388850028 x 361075035 x 288860040 x 252752544 x 229775050 x 202202052 x 194425055 x 183820056 x 180537565 x 155540070 x 144430077 x 131300088 x 114887591 x 1111000100 x 1011010101 x 1001000104 x 972125110 x 919100125 x 808808130 x 777700140 x 722150143 x 707000154 x 656500175 x 577720182 x 555500200 x 505505202 x 500500220 x 459550250 x 404404260 x 388850275 x 367640280 x 361075286 x 353500308 x 328250325 x 311080350 x 288860364 x 277750385 x 262600404 x 250250440 x 229775455 x 222200500 x 202202505 x 200200520 x 194425550 x 183820572 x 176750616 x 164125650 x 155540700 x 144430707 x 143000715 x 141400728 x 138875770 x 131300808 x 125125875 x 115544910 x 1111001000 x 1011011001 x 1010001010 x 1001001100 x 919101111 x 910001144 x 883751300 x 777701313 x 770001375 x 735281400 x 722151414 x 715001430 x 707001540 x 656501625 x 622161750 x 577721820 x 555501925 x 525202002 x 505002020 x 500502200 x 459552222 x 455002275 x 444402525 x 400402600 x 388852626 x 385002750 x 367642828 x 357502860 x 353503080 x 328253250 x 311083500 x 288863535 x 286003575 x 282803640 x 277753850 x 262604004 x 252504040 x 250254444 x 227504550 x 222205005 x 202005050 x 200205252 x 192505500 x 183825555 x 182005656 x 178755720 x 176756500 x 155546565 x 154007000 x 144437070 x 143007150 x 141407700 x 131307777 x 130008008 x 126258888 x 113759100 x 111109191 x 110009625 x 1050410010 x 10100
Negative: -1 x -101101000-2 x -50550500-4 x -25275250-5 x -20220200-7 x -14443000-8 x -12637625-10 x -10110100-11 x -9191000-13 x -7777000-14 x -7221500-20 x -5055050-22 x -4595500-25 x -4044040-26 x -3888500-28 x -3610750-35 x -2888600-40 x -2527525-44 x -2297750-50 x -2022020-52 x -1944250-55 x -1838200-56 x -1805375-65 x -1555400-70 x -1444300-77 x -1313000-88 x -1148875-91 x -1111000-100 x -1011010-101 x -1001000-104 x -972125-110 x -919100-125 x -808808-130 x -777700-140 x -722150-143 x -707000-154 x -656500-175 x -577720-182 x -555500-200 x -505505-202 x -500500-220 x -459550-250 x -404404-260 x -388850-275 x -367640-280 x -361075-286 x -353500-308 x -328250-325 x -311080-350 x -288860-364 x -277750-385 x -262600-404 x -250250-440 x -229775-455 x -222200-500 x -202202-505 x -200200-520 x -194425-550 x -183820-572 x -176750-616 x -164125-650 x -155540-700 x -144430-707 x -143000-715 x -141400-728 x -138875-770 x -131300-808 x -125125-875 x -115544-910 x -111100-1000 x -101101-1001 x -101000-1010 x -100100-1100 x -91910-1111 x -91000-1144 x -88375-1300 x -77770-1313 x -77000-1375 x -73528-1400 x -72215-1414 x -71500-1430 x -70700-1540 x -65650-1625 x -62216-1750 x -57772-1820 x -55550-1925 x -52520-2002 x -50500-2020 x -50050-2200 x -45955-2222 x -45500-2275 x -44440-2525 x -40040-2600 x -38885-2626 x -38500-2750 x -36764-2828 x -35750-2860 x -35350-3080 x -32825-3250 x -31108-3500 x -28886-3535 x -28600-3575 x -28280-3640 x -27775-3850 x -26260-4004 x -25250-4040 x -25025-4444 x -22750-4550 x -22220-5005 x -20200-5050 x -20020-5252 x -19250-5500 x -18382-5555 x -18200-5656 x -17875-5720 x -17675-6500 x -15554-6565 x -15400-7000 x -14443-7070 x -14300-7150 x -14140-7700 x -13130-7777 x -13000-8008 x -12625-8888 x -11375-9100 x -11110-9191 x -11000-9625 x -10504-10010 x -10100


How do I find the factor combinations of the number 101,101,000?

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 101,101,000, 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.

1 101,101,000
-1 -101,101,000

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 101,101,000.

Example:
1 x 101,101,000 = 101,101,000
and
-1 x -101,101,000 = 101,101,000
Notice both answers equal 101,101,000

With that explanation out of the way, let's continue. Next, we take the number 101,101,000 and divide it by 2:

101,101,000 ÷ 2 = 50,550,500

If the quotient is a whole number, then 2 and 50,550,500 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 50,550,500 101,101,000
-1 -2 -50,550,500 -101,101,000

Now, we try dividing 101,101,000 by 3:

101,101,000 ÷ 3 = 33,700,333.3333

If the quotient is a whole number, then 3 and 33,700,333.3333 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 50,550,500 101,101,000
-1 -2 -50,550,500 -101,101,000

Let's try dividing by 4:

101,101,000 ÷ 4 = 25,275,250

If the quotient is a whole number, then 4 and 25,275,250 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 4 25,275,250 50,550,500 101,101,000
-1 -2 -4 -25,275,250 -50,550,500 101,101,000
Keep dividing by the next highest number until you cannot divide anymore.

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

1245781011131420222526283540445052555665707788911001011041101251301401431541751822002022202502602752802863083253503643854044404555005055205505726166507007077157287708088759101,0001,0011,0101,1001,1111,1441,3001,3131,3751,4001,4141,4301,5401,6251,7501,8201,9252,0022,0202,2002,2222,2752,5252,6002,6262,7502,8282,8603,0803,2503,5003,5353,5753,6403,8504,0044,0404,4444,5505,0055,0505,2525,5005,5555,6565,7206,5006,5657,0007,0707,1507,7007,7778,0088,8889,1009,1919,62510,01010,10010,50411,00011,11011,37512,62513,00013,13014,14014,30014,44315,40015,55417,67517,87518,20018,38219,25020,02020,20022,22022,75025,02525,25026,26027,77528,28028,60028,88631,10832,82535,35035,75036,76438,50038,88540,04044,44045,50045,95550,05050,50052,52055,55057,77262,21665,65070,70071,50072,21573,52877,00077,77088,37591,00091,910100,100101,000101,101111,100115,544125,125131,300138,875141,400143,000144,430155,540164,125176,750183,820194,425200,200202,202222,200229,775250,250262,600277,750288,860311,080328,250353,500361,075367,640388,850404,404459,550500,500505,505555,500577,720656,500707,000722,150777,700808,808919,100972,1251,001,0001,011,0101,111,0001,148,8751,313,0001,444,3001,555,4001,805,3751,838,2001,944,2502,022,0202,297,7502,527,5252,888,6003,610,7503,888,5004,044,0404,595,5005,055,0507,221,5007,777,0009,191,00010,110,10012,637,62514,443,00020,220,20025,275,25050,550,500101,101,000
-1-2-4-5-7-8-10-11-13-14-20-22-25-26-28-35-40-44-50-52-55-56-65-70-77-88-91-100-101-104-110-125-130-140-143-154-175-182-200-202-220-250-260-275-280-286-308-325-350-364-385-404-440-455-500-505-520-550-572-616-650-700-707-715-728-770-808-875-910-1,000-1,001-1,010-1,100-1,111-1,144-1,300-1,313-1,375-1,400-1,414-1,430-1,540-1,625-1,750-1,820-1,925-2,002-2,020-2,200-2,222-2,275-2,525-2,600-2,626-2,750-2,828-2,860-3,080-3,250-3,500-3,535-3,575-3,640-3,850-4,004-4,040-4,444-4,550-5,005-5,050-5,252-5,500-5,555-5,656-5,720-6,500-6,565-7,000-7,070-7,150-7,700-7,777-8,008-8,888-9,100-9,191-9,625-10,010-10,100-10,504-11,000-11,110-11,375-12,625-13,000-13,130-14,140-14,300-14,443-15,400-15,554-17,675-17,875-18,200-18,382-19,250-20,020-20,200-22,220-22,750-25,025-25,250-26,260-27,775-28,280-28,600-28,886-31,108-32,825-35,350-35,750-36,764-38,500-38,885-40,040-44,440-45,500-45,955-50,050-50,500-52,520-55,550-57,772-62,216-65,650-70,700-71,500-72,215-73,528-77,000-77,770-88,375-91,000-91,910-100,100-101,000-101,101-111,100-115,544-125,125-131,300-138,875-141,400-143,000-144,430-155,540-164,125-176,750-183,820-194,425-200,200-202,202-222,200-229,775-250,250-262,600-277,750-288,860-311,080-328,250-353,500-361,075-367,640-388,850-404,404-459,550-500,500-505,505-555,500-577,720-656,500-707,000-722,150-777,700-808,808-919,100-972,125-1,001,000-1,011,010-1,111,000-1,148,875-1,313,000-1,444,300-1,555,400-1,805,375-1,838,200-1,944,250-2,022,020-2,297,750-2,527,525-2,888,600-3,610,750-3,888,500-4,044,040-4,595,500-5,055,050-7,221,500-7,777,000-9,191,000-10,110,100-12,637,625-14,443,000-20,220,200-25,275,250-50,550,500-101,101,000

More Examples

Here are some more numbers to try:

101,100,998101,100,999101,101,001101,101,002
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