Divisible Dates












7












$begingroup$


The day of the month, and the month of the year, often divide the year. Most recently it happened on January 3, 2019 because both 1 (January) and 3 divide 2019.



In our era, since 1/1/1, which years have had the most such dates?






arithmetic







share|improve this question









$endgroup$












  • $begingroup$
    For clarification: Is a divisible date one in which either the day or month divide the year, or one in with both do?
    $endgroup$
    – Van
    4 hours ago










  • $begingroup$
    @Van Yes, both.
    $endgroup$
    – Bernardo Recamán Santos
    4 hours ago










  • $begingroup$
    can we solve this with some code? :)
    $endgroup$
    – Flying_whale
    4 hours ago










  • $begingroup$
    @Flying_whale: Go!
    $endgroup$
    – Bernardo Recamán Santos
    4 hours ago
















7












$begingroup$


The day of the month, and the month of the year, often divide the year. Most recently it happened on January 3, 2019 because both 1 (January) and 3 divide 2019.



In our era, since 1/1/1, which years have had the most such dates?






arithmetic







share|improve this question









$endgroup$












  • $begingroup$
    For clarification: Is a divisible date one in which either the day or month divide the year, or one in with both do?
    $endgroup$
    – Van
    4 hours ago










  • $begingroup$
    @Van Yes, both.
    $endgroup$
    – Bernardo Recamán Santos
    4 hours ago










  • $begingroup$
    can we solve this with some code? :)
    $endgroup$
    – Flying_whale
    4 hours ago










  • $begingroup$
    @Flying_whale: Go!
    $endgroup$
    – Bernardo Recamán Santos
    4 hours ago














7












7








7





$begingroup$


The day of the month, and the month of the year, often divide the year. Most recently it happened on January 3, 2019 because both 1 (January) and 3 divide 2019.



In our era, since 1/1/1, which years have had the most such dates?






arithmetic







share|improve this question









$endgroup$




The day of the month, and the month of the year, often divide the year. Most recently it happened on January 3, 2019 because both 1 (January) and 3 divide 2019.



In our era, since 1/1/1, which years have had the most such dates?






arithmetic




arithmetic






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked 4 hours ago









Bernardo Recamán SantosBernardo Recamán Santos

2,3731242




2,3731242












  • $begingroup$
    For clarification: Is a divisible date one in which either the day or month divide the year, or one in with both do?
    $endgroup$
    – Van
    4 hours ago










  • $begingroup$
    @Van Yes, both.
    $endgroup$
    – Bernardo Recamán Santos
    4 hours ago










  • $begingroup$
    can we solve this with some code? :)
    $endgroup$
    – Flying_whale
    4 hours ago










  • $begingroup$
    @Flying_whale: Go!
    $endgroup$
    – Bernardo Recamán Santos
    4 hours ago


















  • $begingroup$
    For clarification: Is a divisible date one in which either the day or month divide the year, or one in with both do?
    $endgroup$
    – Van
    4 hours ago










  • $begingroup$
    @Van Yes, both.
    $endgroup$
    – Bernardo Recamán Santos
    4 hours ago










  • $begingroup$
    can we solve this with some code? :)
    $endgroup$
    – Flying_whale
    4 hours ago










  • $begingroup$
    @Flying_whale: Go!
    $endgroup$
    – Bernardo Recamán Santos
    4 hours ago
















$begingroup$
For clarification: Is a divisible date one in which either the day or month divide the year, or one in with both do?
$endgroup$
– Van
4 hours ago




$begingroup$
For clarification: Is a divisible date one in which either the day or month divide the year, or one in with both do?
$endgroup$
– Van
4 hours ago












$begingroup$
@Van Yes, both.
$endgroup$
– Bernardo Recamán Santos
4 hours ago




$begingroup$
@Van Yes, both.
$endgroup$
– Bernardo Recamán Santos
4 hours ago












$begingroup$
can we solve this with some code? :)
$endgroup$
– Flying_whale
4 hours ago




$begingroup$
can we solve this with some code? :)
$endgroup$
– Flying_whale
4 hours ago












$begingroup$
@Flying_whale: Go!
$endgroup$
– Bernardo Recamán Santos
4 hours ago




$begingroup$
@Flying_whale: Go!
$endgroup$
– Bernardo Recamán Santos
4 hours ago










4 Answers
4






active

oldest

votes


















8












$begingroup$

I'm going to go with




1680




factors:




1,2,3,4,5,6,7,8,10,12,14,15,16,20,21,24,28,30




So it hits on




179 days (10 months times 18 days, minus 30th of February)




Method:



Looked up




Highly composite numbers, picked the largest that's smaller than 2019.







share|improve this answer









$endgroup$





















    5












    $begingroup$

    I found




    with a bit of code i found 1680 with 179 dates you can run it here : https://rextester.com/YITA38880







    share|improve this answer











    $endgroup$





















      4












      $begingroup$

      I'd be surprised if you can beat:




      1080. It equals $2^3times3^3times5$, and so covers $1,2,3,4,5,6,8,9,10,12,15,18,20,24,27,30$ for days and $1,2,3,4,5,6,8,9,10,12$ for months.







      share|improve this answer









      $endgroup$





















        4












        $begingroup$

        I believe I can beat JonMark Perry's answer:




        1260 = 2 x2 x3 x3 x5 x7


        For months, I can get 1, 2, 3, 4, 5, 6, 7, 9, 10, & 12 (10 - same).


        But for days, I get:


        1, 2, 3, 4, 5, 6, 7, 9, 10, 12 & 14, 15, 18, 20, 21, 28, 30 (17 - one more than Jon)







        share|improve this answer









        $endgroup$













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          4 Answers
          4






          active

          oldest

          votes








          4 Answers
          4






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          8












          $begingroup$

          I'm going to go with




          1680




          factors:




          1,2,3,4,5,6,7,8,10,12,14,15,16,20,21,24,28,30




          So it hits on




          179 days (10 months times 18 days, minus 30th of February)




          Method:



          Looked up




          Highly composite numbers, picked the largest that's smaller than 2019.







          share|improve this answer









          $endgroup$


















            8












            $begingroup$

            I'm going to go with




            1680




            factors:




            1,2,3,4,5,6,7,8,10,12,14,15,16,20,21,24,28,30




            So it hits on




            179 days (10 months times 18 days, minus 30th of February)




            Method:



            Looked up




            Highly composite numbers, picked the largest that's smaller than 2019.







            share|improve this answer









            $endgroup$
















              8












              8








              8





              $begingroup$

              I'm going to go with




              1680




              factors:




              1,2,3,4,5,6,7,8,10,12,14,15,16,20,21,24,28,30




              So it hits on




              179 days (10 months times 18 days, minus 30th of February)




              Method:



              Looked up




              Highly composite numbers, picked the largest that's smaller than 2019.







              share|improve this answer









              $endgroup$



              I'm going to go with




              1680




              factors:




              1,2,3,4,5,6,7,8,10,12,14,15,16,20,21,24,28,30




              So it hits on




              179 days (10 months times 18 days, minus 30th of February)




              Method:



              Looked up




              Highly composite numbers, picked the largest that's smaller than 2019.








              share|improve this answer












              share|improve this answer



              share|improve this answer










              answered 3 hours ago









              BassBass

              28.5k469175




              28.5k469175























                  5












                  $begingroup$

                  I found




                  with a bit of code i found 1680 with 179 dates you can run it here : https://rextester.com/YITA38880







                  share|improve this answer











                  $endgroup$


















                    5












                    $begingroup$

                    I found




                    with a bit of code i found 1680 with 179 dates you can run it here : https://rextester.com/YITA38880







                    share|improve this answer











                    $endgroup$
















                      5












                      5








                      5





                      $begingroup$

                      I found




                      with a bit of code i found 1680 with 179 dates you can run it here : https://rextester.com/YITA38880







                      share|improve this answer











                      $endgroup$



                      I found




                      with a bit of code i found 1680 with 179 dates you can run it here : https://rextester.com/YITA38880








                      share|improve this answer














                      share|improve this answer



                      share|improve this answer








                      edited 11 secs ago

























                      answered 3 hours ago









                      Flying_whaleFlying_whale

                      1,559123




                      1,559123























                          4












                          $begingroup$

                          I'd be surprised if you can beat:




                          1080. It equals $2^3times3^3times5$, and so covers $1,2,3,4,5,6,8,9,10,12,15,18,20,24,27,30$ for days and $1,2,3,4,5,6,8,9,10,12$ for months.







                          share|improve this answer









                          $endgroup$


















                            4












                            $begingroup$

                            I'd be surprised if you can beat:




                            1080. It equals $2^3times3^3times5$, and so covers $1,2,3,4,5,6,8,9,10,12,15,18,20,24,27,30$ for days and $1,2,3,4,5,6,8,9,10,12$ for months.







                            share|improve this answer









                            $endgroup$
















                              4












                              4








                              4





                              $begingroup$

                              I'd be surprised if you can beat:




                              1080. It equals $2^3times3^3times5$, and so covers $1,2,3,4,5,6,8,9,10,12,15,18,20,24,27,30$ for days and $1,2,3,4,5,6,8,9,10,12$ for months.







                              share|improve this answer









                              $endgroup$



                              I'd be surprised if you can beat:




                              1080. It equals $2^3times3^3times5$, and so covers $1,2,3,4,5,6,8,9,10,12,15,18,20,24,27,30$ for days and $1,2,3,4,5,6,8,9,10,12$ for months.








                              share|improve this answer












                              share|improve this answer



                              share|improve this answer










                              answered 4 hours ago









                              JonMark PerryJonMark Perry

                              18.6k63888




                              18.6k63888























                                  4












                                  $begingroup$

                                  I believe I can beat JonMark Perry's answer:




                                  1260 = 2 x2 x3 x3 x5 x7


                                  For months, I can get 1, 2, 3, 4, 5, 6, 7, 9, 10, & 12 (10 - same).


                                  But for days, I get:


                                  1, 2, 3, 4, 5, 6, 7, 9, 10, 12 & 14, 15, 18, 20, 21, 28, 30 (17 - one more than Jon)







                                  share|improve this answer









                                  $endgroup$


















                                    4












                                    $begingroup$

                                    I believe I can beat JonMark Perry's answer:




                                    1260 = 2 x2 x3 x3 x5 x7


                                    For months, I can get 1, 2, 3, 4, 5, 6, 7, 9, 10, & 12 (10 - same).


                                    But for days, I get:


                                    1, 2, 3, 4, 5, 6, 7, 9, 10, 12 & 14, 15, 18, 20, 21, 28, 30 (17 - one more than Jon)







                                    share|improve this answer









                                    $endgroup$
















                                      4












                                      4








                                      4





                                      $begingroup$

                                      I believe I can beat JonMark Perry's answer:




                                      1260 = 2 x2 x3 x3 x5 x7


                                      For months, I can get 1, 2, 3, 4, 5, 6, 7, 9, 10, & 12 (10 - same).


                                      But for days, I get:


                                      1, 2, 3, 4, 5, 6, 7, 9, 10, 12 & 14, 15, 18, 20, 21, 28, 30 (17 - one more than Jon)







                                      share|improve this answer









                                      $endgroup$



                                      I believe I can beat JonMark Perry's answer:




                                      1260 = 2 x2 x3 x3 x5 x7


                                      For months, I can get 1, 2, 3, 4, 5, 6, 7, 9, 10, & 12 (10 - same).


                                      But for days, I get:


                                      1, 2, 3, 4, 5, 6, 7, 9, 10, 12 & 14, 15, 18, 20, 21, 28, 30 (17 - one more than Jon)








                                      share|improve this answer












                                      share|improve this answer



                                      share|improve this answer










                                      answered 4 hours ago









                                      VanVan

                                      3414




                                      3414






























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