Find some digits of factorial 17












7












$begingroup$


$17!$ is equal to $$35568x428096y00$$
Both x and y, are digits. Find x,y.



So, $$17!=2^{15}*3^6*5^3*7^2*11*13*17=(2^3*5^3)*2^{12}*3^6*7^2*11*13*17$$
If there`s a product of $(2*5)^3$



Then this number has $3$ zeros at the end, so $y=0$



How do I find the $x$ now?






elementary-number-theory factorial







share|cite|improve this question









New contributor




a_man_with_no_name is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$

















    7












    $begingroup$


    $17!$ is equal to $$35568x428096y00$$
    Both x and y, are digits. Find x,y.



    So, $$17!=2^{15}*3^6*5^3*7^2*11*13*17=(2^3*5^3)*2^{12}*3^6*7^2*11*13*17$$
    If there`s a product of $(2*5)^3$



    Then this number has $3$ zeros at the end, so $y=0$



    How do I find the $x$ now?






    elementary-number-theory factorial







    share|cite|improve this question









    New contributor




    a_man_with_no_name is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.







    $endgroup$















      7












      7








      7





      $begingroup$


      $17!$ is equal to $$35568x428096y00$$
      Both x and y, are digits. Find x,y.



      So, $$17!=2^{15}*3^6*5^3*7^2*11*13*17=(2^3*5^3)*2^{12}*3^6*7^2*11*13*17$$
      If there`s a product of $(2*5)^3$



      Then this number has $3$ zeros at the end, so $y=0$



      How do I find the $x$ now?






      elementary-number-theory factorial







      share|cite|improve this question









      New contributor




      a_man_with_no_name is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.







      $endgroup$




      $17!$ is equal to $$35568x428096y00$$
      Both x and y, are digits. Find x,y.



      So, $$17!=2^{15}*3^6*5^3*7^2*11*13*17=(2^3*5^3)*2^{12}*3^6*7^2*11*13*17$$
      If there`s a product of $(2*5)^3$



      Then this number has $3$ zeros at the end, so $y=0$



      How do I find the $x$ now?






      elementary-number-theory factorial




      elementary-number-theory factorial






      share|cite|improve this question









      New contributor




      a_man_with_no_name is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      share|cite|improve this question









      New contributor




      a_man_with_no_name is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      share|cite|improve this question




      share|cite|improve this question








      edited 3 hours ago









      J. W. Tanner

      2,6271217




      2,6271217






      New contributor




      a_man_with_no_name is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      asked 3 hours ago









      a_man_with_no_namea_man_with_no_name

      823




      823




      New contributor




      a_man_with_no_name is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.





      New contributor





      a_man_with_no_name is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.






      a_man_with_no_name is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.






















          2 Answers
          2






          active

          oldest

          votes


















          13












          $begingroup$

          HINT $17!$ is divisible by $9$. What is an easy test for divisibility by 9, involving the digits of a number?






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            The sum od its digits Has to be divisible by 9
            $endgroup$
            – a_man_with_no_name
            3 hours ago










          • $begingroup$
            How could i miss it!
            $endgroup$
            – a_man_with_no_name
            3 hours ago



















          5












          $begingroup$

          The alternating sum of digits must be divisible by $11$, i.e., $11mid 18-x$. It follows that $x=7$.






          share|cite|improve this answer









          $endgroup$













            Your Answer





            StackExchange.ifUsing("editor", function () {
            return StackExchange.using("mathjaxEditing", function () {
            StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
            StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
            });
            });
            }, "mathjax-editing");

            StackExchange.ready(function() {
            var channelOptions = {
            tags: "".split(" "),
            id: "69"
            };
            initTagRenderer("".split(" "), "".split(" "), channelOptions);

            StackExchange.using("externalEditor", function() {
            // Have to fire editor after snippets, if snippets enabled
            if (StackExchange.settings.snippets.snippetsEnabled) {
            StackExchange.using("snippets", function() {
            createEditor();
            });
            }
            else {
            createEditor();
            }
            });

            function createEditor() {
            StackExchange.prepareEditor({
            heartbeatType: 'answer',
            autoActivateHeartbeat: false,
            convertImagesToLinks: true,
            noModals: true,
            showLowRepImageUploadWarning: true,
            reputationToPostImages: 10,
            bindNavPrevention: true,
            postfix: "",
            imageUploader: {
            brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
            contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
            allowUrls: true
            },
            noCode: true, onDemand: true,
            discardSelector: ".discard-answer"
            ,immediatelyShowMarkdownHelp:true
            });


            }
            });






            a_man_with_no_name is a new contributor. Be nice, and check out our Code of Conduct.










            draft saved

            draft discarded


















            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3130579%2ffind-some-digits-of-factorial-17%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown

























            2 Answers
            2






            active

            oldest

            votes








            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            13












            $begingroup$

            HINT $17!$ is divisible by $9$. What is an easy test for divisibility by 9, involving the digits of a number?






            share|cite|improve this answer









            $endgroup$













            • $begingroup$
              The sum od its digits Has to be divisible by 9
              $endgroup$
              – a_man_with_no_name
              3 hours ago










            • $begingroup$
              How could i miss it!
              $endgroup$
              – a_man_with_no_name
              3 hours ago
















            13












            $begingroup$

            HINT $17!$ is divisible by $9$. What is an easy test for divisibility by 9, involving the digits of a number?






            share|cite|improve this answer









            $endgroup$













            • $begingroup$
              The sum od its digits Has to be divisible by 9
              $endgroup$
              – a_man_with_no_name
              3 hours ago










            • $begingroup$
              How could i miss it!
              $endgroup$
              – a_man_with_no_name
              3 hours ago














            13












            13








            13





            $begingroup$

            HINT $17!$ is divisible by $9$. What is an easy test for divisibility by 9, involving the digits of a number?






            share|cite|improve this answer









            $endgroup$



            HINT $17!$ is divisible by $9$. What is an easy test for divisibility by 9, involving the digits of a number?







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered 3 hours ago









            Mark FischlerMark Fischler

            32.7k12252




            32.7k12252












            • $begingroup$
              The sum od its digits Has to be divisible by 9
              $endgroup$
              – a_man_with_no_name
              3 hours ago










            • $begingroup$
              How could i miss it!
              $endgroup$
              – a_man_with_no_name
              3 hours ago


















            • $begingroup$
              The sum od its digits Has to be divisible by 9
              $endgroup$
              – a_man_with_no_name
              3 hours ago










            • $begingroup$
              How could i miss it!
              $endgroup$
              – a_man_with_no_name
              3 hours ago
















            $begingroup$
            The sum od its digits Has to be divisible by 9
            $endgroup$
            – a_man_with_no_name
            3 hours ago




            $begingroup$
            The sum od its digits Has to be divisible by 9
            $endgroup$
            – a_man_with_no_name
            3 hours ago












            $begingroup$
            How could i miss it!
            $endgroup$
            – a_man_with_no_name
            3 hours ago




            $begingroup$
            How could i miss it!
            $endgroup$
            – a_man_with_no_name
            3 hours ago











            5












            $begingroup$

            The alternating sum of digits must be divisible by $11$, i.e., $11mid 18-x$. It follows that $x=7$.






            share|cite|improve this answer









            $endgroup$


















              5












              $begingroup$

              The alternating sum of digits must be divisible by $11$, i.e., $11mid 18-x$. It follows that $x=7$.






              share|cite|improve this answer









              $endgroup$
















                5












                5








                5





                $begingroup$

                The alternating sum of digits must be divisible by $11$, i.e., $11mid 18-x$. It follows that $x=7$.






                share|cite|improve this answer









                $endgroup$



                The alternating sum of digits must be divisible by $11$, i.e., $11mid 18-x$. It follows that $x=7$.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered 3 hours ago









                Dietrich BurdeDietrich Burde

                80k647103




                80k647103






















                    a_man_with_no_name is a new contributor. Be nice, and check out our Code of Conduct.










                    draft saved

                    draft discarded


















                    a_man_with_no_name is a new contributor. Be nice, and check out our Code of Conduct.













                    a_man_with_no_name is a new contributor. Be nice, and check out our Code of Conduct.












                    a_man_with_no_name is a new contributor. Be nice, and check out our Code of Conduct.
















                    Thanks for contributing an answer to Mathematics Stack Exchange!


                    • Please be sure to answer the question. Provide details and share your research!

                    But avoid …



                    • Asking for help, clarification, or responding to other answers.

                    • Making statements based on opinion; back them up with references or personal experience.


                    Use MathJax to format equations. MathJax reference.


                    To learn more, see our tips on writing great answers.




                    draft saved


                    draft discarded














                    StackExchange.ready(
                    function () {
                    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3130579%2ffind-some-digits-of-factorial-17%23new-answer', 'question_page');
                    }
                    );

                    Post as a guest















                    Required, but never shown





















































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown

































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown







                    -

                    Popular posts from this blog

                    How to label and detect the document text images

                    Image
                    1 $begingroup$ This is what I mean as document text image: I want to label the texts in image as separate blocks and my model should detect these labels as classes. NOTE: This is how the end result should be like: The labels like Block 1, Block 2, Block 3,.. should be Logo, Title, Date,.. Others, etc. Work done: First approach : I tried to implement this method via Object Detection, it didn't work. It didn't even detect any text. Second approach : Then I tried it using PixelLink. As this model is build for scene text detection, it detected each and every text in the image. But this method can detect multiple lines of text if the threshold values are increased. But I have no idea how do I add labels to the text blocks. PIXEL_CLS_WEIGHT_all_ones = 'PIXEL_CLS_WEIGHT_all_ones' PIXEL_C...
                    Read more

                    Vallis Paradisi

                    Image
                    Coordinata: .mw-parser-output .geo-default,.mw-parser-output .geo-dms,.mw-parser-output .geo-dec{display:inline}.mw-parser-output .geo-nondefault,.mw-parser-output .geo-multi-punct{display:none}.mw-parser-output .longitude,.mw-parser-output .latitude{white-space:nowrap} 33°03′S 71°37′W  /  33.05°S 71.617°W  / -33.05; -71.617 Vallis Paradisi Res apud Vicidata repertae: Civitas : Chilia Numerus incolarum : 296 655 Zona horaria : UTC-4 Situs interretialis Nomen officiale : Valparaíso Gubernium Consilium : municipal council of Valparaíso Geographia Superficies : 401 600 000 Metrum quadratum Coniunctiones urbium Urbes gemellae : Ovetum , Badalona , Santa Fe , Ora longa , Sciamhaevum , Quantunia , Callao , Bat Yam , Melaka , Novorossiysk , Busan , Corduba , Odessa , Rosario , Malacca , Barcino , Soteropolis , Franciscopolis (California) , Guanajuato, Silao Tabula aut despectus Despectus in portum sinumque et urbem Vallis Paradisi Vallis Para...
                    Read more

                    Tabula Rosettana

                    Image
                    Tabula multilinguis Rosettana in Museo Britannico ostenditur. Tabula Rosettana, [1] etiam titulo OGIS 90 agnita, est stela decreto de rebus sacris in Aegypto anno 196 a.C.n. lato inscripta. Tabula iuxta Rosettam Aegypti, urbem in delta Nili et ad oram maris Mediterranei iacentem, anno 1799 a milite Francico reperta est. Inventio stelae, linguis duabus scripturisque tribus inscriptae, eruditis Instituti Aegypti statim nuntiata est; ibi enim iussu imperatoris Napoleonis eruditi omnium scientiarum (sub aegide Commissionis Scientiarum et Artium) properaverant cum expeditione Francica. Qua a Britannis mox debellata, tabula Rosettana Londinium missa hodie apud Museum Britannicum iacet. Textus Graecus cito lectus interpretationi textuum Aegyptiorum (in formis hieroglyphica et demotica expressorum) gradatim adiuvit. Denique textum plene interpretatus est Ioannes Franciscus Champollion. Ab opere eruditorum cumulativo coepit hodiernus scripturae hieroglyphicae linguaeque Aegyptiae a...
                    Read more