[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-362262-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-362262-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","factors-multiples-prime-numbers-directions-answer-key","Factors, Multiples - Prime Numbers - Directions Answer Key","","Worksheet for mastering factors, multiples, and prime numbers through 21 targeted math questions. Students list factors, identify primes and composites, perform prime factorization, and compute GCF and LCM for given pairs of integers. The set also includes exponent-based prime factorization, finding common multiples, comparing which number has more factors, and solving a community garden challenge using LCM and GCF. An answer key provides completed solutions for each item.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/factors-multiples-prime-numbers-directions-answer-key/362262/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/factors-multiples-prime-numbers-directions-answer-key/362262.png","ImageObject",300,407,{"name":42,"@type":43},"Aran","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-28","2026-09-23",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",15,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How do you find all factors of a number like 48?","Question",{"text":63,"@type":64},"List the whole numbers that divide the number evenly. For 48, the answer key lists all factors from 1 up to 48 that divide without remainder.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What is the difference between prime and composite numbers?",{"text":68,"@type":64},"Prime numbers have exactly two factors: 1 and the number itself, while composite numbers have more than two factors. The worksheet asks students to identify primes among given options and circle the composites.",{"name":70,"@type":61,"acceptedAnswer":71},"How are GCF and LCM used in the challenge problem?",{"text":72,"@type":64},"Use LCM to find when two repeating events occur together, based on the intervals (18 and 30 days). Use GCF to determine the greatest number of equal-sized teams from volunteer counts (120 and 150).","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},362262,1790370101,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":96,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":30,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":144,"read_time":111,"preview_page_count":4},137455076865,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Name:     \nFactors, Multiples, & Prime Numbers Directions: Answer each question. Show work where needed.  \n1.) List all factors of 48:    \n2.) Is 89 a prime number?    \n3.) List the first 5 multiples of 16:    \n4.) What is the prime factorization of 84?    \n5.) Find the GCF of 56 and 72:    \n6.) What is the LCM of 8 and 15?    \n7.) Which of the following numbers are prime?  \n17, 51, 53, 77 →    \n8.) Which number is a common multiple of both 9 and 12?  \n18, 24, 36, 48 →    \n9.) Write the prime factorization of 90 using exponents:    \n10.) Circle all composite numbers:  \n29 31 33 35 37  \n11.) What is the GCF of 66 and 99?    \n12.) Find the LCM of 10 and 12:    \n13.) Is 117 a prime or composite number?    \n14.) Which number is a factor of both 60 and 84?  \n6, 8, 10, 14 → _______________  \n15.) What is the smallest odd prime number? _______________  \n16.) List all prime numbers between 40 and 60: ___________________________  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at ](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)[www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) 1  \n17.) Which has more factors: 42 or 54?    \n18.) What is the product of the first four prime numbers?    \n19.) Write a number that has exactly four distinct prime factors    \n20.) A school has 72 students in Math Club and 90 in Science Club. What’s the greatest number of equal teams they can be split into with no one left out?  \n21.) Challenge Problem:  \nA community garden schedules events:  \n• Planting Days are every 18 days  \n• Watering Days are every 30 days  \n• Both occur today.  \na.) When is the next day both events will happen on the same day?    \nb.) If 120 volunteers attend Planting Days and 150 attend Watering Days, how many equal-sized teams can be formed from each group?  \nc.) How many total teams will there be?    \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at ](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)[www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) 2  \nANSWER KEY  \n1.) 1, 2, 3, 4, 6, 8, 12, 16, 24, 48  \n2.) Yes  \n3.) 16, 32, 48, 64, 80  \n4.) 2² × 3 × 7 5.) 8  \n6.) 120 7.) 17, 53 8.) 36  \n9.) 2 × 3² × 5 10.) 33, 35 11.) 33  \n12.) 60  \n13.) Composite 14.) 6  \n15.) 3  \n16.) 41, 43, 47, 53, 59  \n17.) 54 (8 factors vs. 6 for 42)  \n18.) 2 × 3 × 5 × 7 = 210  \n19.) 210 (2 × 3 × 5 × 7), or any such example  \n20.) GCF of 72 and 90 = 18  \nChallenge Problem:  \na.) LCM of 18 and 30 = 90 days  \nb.) GCF of 120 and 150 = 30 volunteers per team  \nc.) 120 ÷ 30 = 4 teams (Planting), 150 ÷ 30 = 5 teams (Watering), Total teams = 9  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at ](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)[www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) 3","cbCaiuIXm4Ec6Bco","https://ap.wps.com/l/cbCaiuIXm4Ec6Bco","pdf",576790,"English","# Directions\n## Questions 1-21\n# Answer Key","[{\"question\":\"How do you find all factors of a number like 48?\",\"answer\":\"List the whole numbers that divide the number evenly. For 48, the answer key lists all factors from 1 up to 48 that divide without remainder.\"},{\"question\":\"What is the difference between prime and composite numbers?\",\"answer\":\"Prime numbers have exactly two factors: 1 and the number itself, while composite numbers have more than two factors. The worksheet asks students to identify primes among given options and circle the composites.\"},{\"question\":\"How are GCF and LCM used in the challenge problem?\",\"answer\":\"Use LCM to find when two repeating events occur together, based on the intervals (18 and 30 days). Use GCF to determine the greatest number of equal-sized teams from volunteer counts (120 and 150).\"}]","Factors, Multiples - Prime Numbers - Directions Answer Key | PDF",1790146914]