[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-362265-105":59,"doc-detail-362265-en":131},{"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":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","factors-multiples-prime-numbers-directions-answer-each-question","Factors, Multiples & Prime Numbers - Directions - Answer Each Question","","Worksheet directions and an answer key covering foundational number theory skills: listing factors and multiples, identifying prime versus composite numbers, performing prime factorizations using exponents, and finding GCF and LCM for given pairs. Includes multi-part challenge work using LCM and GCF for meeting schedules and forming teams with equal runner counts, plus requests to compare factor counts between numbers.",{"@graph":69,"@context":123},[70,84,106],{"@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/factors-multiples-prime-numbers-directions-answer-each-question/362265/",{"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/factors-multiples-prime-numbers-directions-answer-each-question/362265.png","ImageObject",300,407,{"name":92,"@type":93},"Aran","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-09-23",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",15,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you find all factors of a number like 60?","Question",{"text":113,"@type":114},"List the positive integers that divide the number evenly. For 60, the factors include 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What is the difference between a prime number and a composite number?",{"text":118,"@type":114},"A prime number has exactly two factors: 1 and itself, while a composite number has more than two factors. For example, 91 is not prime because 91 = 7 × 13.",{"name":120,"@type":111,"acceptedAnswer":121},"How are GCF and LCM used in the challenge problem?",{"text":122,"@type":114},"Use LCM to find when two repeating events happen again and use GCF to determine the greatest equal team size. The schedule repeats every LCM(20, 30) = 60 days, and the largest equal team size is GCF(180, 210) = 30 runners per team.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},362265,1790241287,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"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":39,"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 60:    \n2.) Is 91 a prime number?    \n3.) List the first 5 multiples of 18:    \n4.) What is the prime factorization of 96?    \n5.) Find the GCF of 72 and 108:    \n6.) What is the LCM of 14 and 15?    \n7.) Which of the following numbers are prime?  \n19, 27, 59, 85 →    \n8.) Which number is a common multiple of both 10 and 12?  \n20, 30, 36, 60 →    \n9.) Write the prime factorization of 105 using exponents:    \n10.) Circle all composite numbers:  \n43 44 45 47 49  \n11.) What is the GCF of 90 and 120?    \n12.) Find the LCM of 16 and 20:    \n13.) Is 121 a prime or composite number?    \n14.) Which number is a factor of both 66 and 99?  \n3, 11, 22, 33 → _______________  \n15.) What is the largest prime number less than 50? _______________  \n16.) List all prime numbers between 60 and 80: ___________________________  \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: 64 or 100?    \n18.) What is the product of the first five prime numbers?    \n19.) Write a number that has exactly five distinct prime factors    \n20.) A team has 84 basketballs and 98 cones. What’s the greatest number of equipment kits that can be made using both types of equipment with no extras?  \n21.) Challenge Problem:  \nA marathon club meets for hill runs every 20 days and for interval training every 30 days. They meet for both today.  \na.) In how many days will both types of training fall on the same day again?  \nb.) If 180 runners attend hill runs and 210 attend intervals, and they want to form teams with equal numbers of runners from each, what’s the largest team size possible?  \nc.) How many total teams can they form?  \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, 5, 6, 10, 12, 15, 20, 30, 60  \n2.) No (91 = 7 × 13) 3.) 18, 36, 54, 72, 90  \n4.) 2⁵ × 3 5.) 36 6.) 210 7.) 19, 59 8.) 60  \n9.) 3 × 5 × 7 10.) 44, 45, 49 11.) 30  \n12.) 80  \n13.) Composite (11 × 11) 14.) 33  \n15.) 47  \n16.) 61, 67, 71, 73, 79  \n17.) 100 (9 factors vs. 7 for 64)  \n18.) 2 × 3 × 5 × 7 × 11 = 2310  \n19.) 2310 (2 × 3 × 5 × 7 × 11)  \n20.) GCF of 84 and 98 = 14  \nChallenge Answer:  \na.) LCM of 20 and 30 = 60 days  \nb.) GCF of 180 and 210 = 30 runners per team  \nc.) 180 ÷ 30 = 6 teams, 210 ÷ 30 = 7 teams → 13 total teams  \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","cbCaiu6bLC50nsJv","https://ap.wps.com/l/cbCaiu6bLC50nsJv","pdf",594878,"English","# Factors, Multiples & Prime Numbers\n## Factor, multiple, prime/composite, and prime factorization questions\n## GCF and LCM questions\n## Composite and factor-identification items\n## Challenge problem (LCM/GCF for schedules and teams)","[{\"question\":\"How do you find all factors of a number like 60?\",\"answer\":\"List the positive integers that divide the number evenly. For 60, the factors include 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.\"},{\"question\":\"What is the difference between a prime number and a composite number?\",\"answer\":\"A prime number has exactly two factors: 1 and itself, while a composite number has more than two factors. For example, 91 is not prime because 91 = 7 × 13.\"},{\"question\":\"How are GCF and LCM used in the challenge problem?\",\"answer\":\"Use LCM to find when two repeating events happen again and use GCF to determine the greatest equal team size. The schedule repeats every LCM(20, 30) = 60 days, and the largest equal team size is GCF(180, 210) = 30 runners per team.\"}]","Factors, Multiples & Prime Numbers - Directions - Answer Each Question | PDF",1790146916]