[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-348149-105":59,"doc-detail-348149-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","gmat-club-math-book-number-theory-study-notes","GMAT Club Math Book - Number Theory - Study Notes","","GMAT Club Math Book provides structured study notes for GMAT quantitative topics, beginning with Number Theory and its core number types: integers, rational (fractions), and irrational numbers. It defines key concepts such as even and odd integers, positive and negative real numbers, and prime versus composite numbers, clarifying exclusions like decimals in integers. The material also covers foundational arithmetic rules for parity and sign, plus examples for irrational values such as √2 and π.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/gmat-club-math-book-number-theory-study-notes/348149/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/gmat-club-math-book-number-theory-study-notes/348149.png","ImageObject",300,407,{"name":92,"@type":93},"Jasmine","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-06","2026-09-22",true,{"@type":102,"interactionType":103,"userInteractionCount":56},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What number types does GMAT focus on for Number Theory?","Question",{"text":112,"@type":113},"GMAT deals with real numbers: integers, fractions (rational numbers), and irrational numbers. These types are treated as distinct categories with no overlap between rational and irrational numbers.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are integers defined in this material?",{"text":117,"@type":113},"Integers are all negative natural numbers, zero, and positive natural numbers. Integers are whole numbers and do not include decimals or fractions.",{"name":119,"@type":110,"acceptedAnswer":120},"What is the difference between prime and composite numbers here?",{"text":121,"@type":113},"A prime number has exactly two distinct natural number divisors: 1 and itself. A composite number can be written as a product of two factors both greater than 1, and 1 is not prime because it has only one divisor.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},348149,1790246770,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":56,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":146,"preview_urls":147},2336478487870,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","For the latest version of the GMAT.BUI \\#Pok, please visit: [http://gmatclub.com/NBUICPPL](http://gmatclub.com/NBUICPPL)  \nGMAT Club’s Other Resources:  \nGMAT Club CAT Tests  \n[gmatclub.com/tests](gmatclub.com/tests)  \nThe Verbal Initiative  \n[gmatclub.com/verbal](gmatclub.com/verbal)  \nGMAT Club Math Book  \n[gmatclub.com/mathbook](gmatclub.com/mathbook)  \nGMAT Toolkit iPad App  \n[gmatclub.com/iPhone](gmatclub.com/iPhone)  \nGMAT Course & Admissions Consultant Reviews  \n[gmatclub.com/reviews](gmatclub.com/reviews)  \nFacebook  \n[facebook.com/](facebook.com/)[ ](facebook.com/)gmatclubforum  \nTable of Contents  \nNumber Theory .................................................................................. 3  \nINTEGERS.................................................................................................. 3  \nIRRATIONAL NUMBERS ................................................................................... 3  \nPOSITIVE AND NEGATIVE NUMBERS .................................................................... 4  \nFRACTIONS ................................................................................................ 9  \nEXPONENTS .............................................................................................. 12  \nLAST DIGIT OF A PRODUCT ............................................................................ 13  \nLAST DIGIT OF A POWER ............................................................................... 13  \nROOTS .................................................................................................... 14  \nPERCENT ................................................................................................. 15  \nAbsolute Value .................................................................................. 17  \nFactorials ......................................................................................... 21  \nAlgebra............................................................................................ 23  \nRemainders ...................................................................................... 27  \nWord Problems Overview ..................................................................... 33  \nDistance/Speed/Time Word Problems ...................................................... 37  \nWork Word Problems ........................................................................... 45  \nAdvanced Overlapping Sets Problems....................................................... 49  \nPolygons .......................................................................................... 66  \nCircles ............................................................................................. 72  \nCoordinate Geometry .......................................................................... 81  \nStandard Deviation ........................................................................... 101  \nProbability ..................................................................................... 105  \nCombinations & Permutations .............................................................. 111  \n3‐D Geometries ................................................................................ 118  \nGMAT Club Math Book  \n‐ 2 ‐ part of GMAT ToolKit iPhone App  \nNumber Theory  \nDefinition  \nNumber Theory is concerned with the properties of numbers in general, and in particular integers.  \nAs this is a huge issue we decided to divide it into smaller topics. Below is the list of Number Theory topics.  \nGMAT Number Types  \nGMAT is dealing only with Real Numbers: Integers, Fractions and Irrational Numbers.  \nINTEGERS  \nDefinition  \nIntegers are defined as: all negative natural numbers , zero , and positive natural  \nnumbers  .  \nNote that integers do not include decimals or fractions ‐ just whole numbers.  \nEven and Odd Numbers  \nAn even number is an integer that is \"evenly divisible\" by 2, i.e. , divisible by 2 without a remainder.  \nAn even number is an integer of the form ","cbCaireK52K4OCqM","https://ap.wps.com/l/cbCaireK52K4OCqM","pdf",3179227,126,"English","# Number Theory\n## GMAT Number Types\n## Integers\n## Positive and Negative Numbers\n## Prime Numbers","[{\"question\":\"What number types does GMAT focus on for Number Theory?\",\"answer\":\"GMAT deals with real numbers: integers, fractions (rational numbers), and irrational numbers. These types are treated as distinct categories with no overlap between rational and irrational numbers.\"},{\"question\":\"How are integers defined in this material?\",\"answer\":\"Integers are all negative natural numbers, zero, and positive natural numbers. Integers are whole numbers and do not include decimals or fractions.\"},{\"question\":\"What is the difference between prime and composite numbers here?\",\"answer\":\"A prime number has exactly two distinct natural number divisors: 1 and itself. 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