[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-359098-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-359098-en":130},{"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-word-problems-answer-key","Factors - Multiples Word Problems - Answer Key","","K-12 math worksheet on factors and multiples using practical garden and seed scenarios. Students solve word problems by listing factor pairs, determining whether a number is a multiple, and explaining reasoning. Tasks include finding row sizes that divide evenly, identifying prime vs. composite numbers, computing LCMs for scheduling, and determining missing factors using complete factor sets. An answer key provides worked results and final checks for all problems.",{"@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-word-problems-answer-key/359098/",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-word-problems-answer-key/359098.png","ImageObject",300,407,{"name":42,"@type":43},"\tJames","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-01","2026-09-23",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",19,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How do you determine factor pairs for a given number in these problems?","Question",{"text":63,"@type":64},"Find all pairs of whole numbers that multiply to the given number. The worksheet shows examples like listing factors for 24 and 28.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How can you tell whether one number is a multiple of another?",{"text":68,"@type":64},"Check whether the larger number is divisible by the given factor with no remainder. For example, 42 is a multiple of 6 because 42 = 6 × 7.",{"name":70,"@type":61,"acceptedAnswer":71},"What does the LCM calculation represent in the scheduling problem?",{"text":72,"@type":64},"The LCM gives the first day both volunteers meet based on their watering intervals. The answer uses LCM(4, 6) = 12 and LCM(3, 5) = 15.","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},359098,1790246847,{"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":55,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":33,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":124,"preview_page_count":4},2336474466412,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Name:    \nFactors & Multiples Word Problems Directions: Read each word problem carefully.  \nFor each problem, use your knowledge of factors and multiples to solve.  \n1.  \nA gardener has 24 tomato plants to arrange in equal rows with no plants left over. List all the ways she can arrange them. (Hint: find all factor pairs of 24 . )  \nAnswer:   2.  \nSeeds are packed in bags of 6. Is 42 a multiple of 6?  \nExplain how you know, then list 3 more multiples of 6 greater than 42.  \nAnswer:   3.  \nA gardener plants 36 sunflowers in equal rows.  \nWhich row sizes work with no extras: 5, 6, 7, 8, or 9? List all that work.  \nAnswer:    \n4.  \nIs 17 prime or composite? A gardener wants to arrange 17 pepper plants in equal rows. Explain why only one arrangement is possible.  \nAnswer:   5.  \nThe garden has 48 carrot seeds to split equally.  \nDo 3, 4, 6, and 8 all work as the number of plots? Show your work for each.  \nAnswer:   6.  \nVolunteer A waters every 4 days. Volunteer B waters every 6 days.  \nIn how many days will they water on the same day? (Find the LCM of 4 and 6. )  \nAnswer:    \n1  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \n7.  \nThere are 32 bean plants to place in equal rows of 2, 4, or 8. How many rows does each arrangement make?  \nAnswer:   8.  \nThe gardener says 15 is a multiple of 4. Is she correct?  \nExplain your reasoning and name the multiples of 4 closest to 15.  \nAnswer:   9.  \nA garden plot has 28 flowers to be arranged in equal rows. List all factor pairs of 28.  \nAnswer:   10.  \nSeeds come in packs of 8. The garden needs exactly 56 seeds. Is 56 a multiple of 8? How many packs are needed?  \nAnswer:   11.  \nTwo gardeners meet at the garden every 3 days and every 5 days respectively. What is the first day both gardeners are at the garden at the same time?  \nAnswer:    \nChallenge Problem – Error Analysis  \nA student solved this problem:  \nA student says the factors of 18 are: 1, 2, 3, 6, and 18.  \nA gardener uses this list to arrange 18 flower pots in equal rows.  \nThe student is missing one factor pair. Identify the missing factor.  \nFind the missing factor, explain what factor pair it completes, and list all factor pairs of 18.  \nCorrect answer:    \n2  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \n3  \nANSWER KEY  \n1. 1×24, 2×12, 3×8, 4×6 (factors of 24: 1, 2, 3, 4, 6, 8, 12, 24)  \n2. Yes. 42 = 6 × 7. Next multiples: 48, 54, 60  \n3. 6 and 9 (36 = 6×6 and 36 = 9×4; not divisible by 5, 7, or 8)  \n4. Prime. 17 has no factors other than 1 and 17. Only 1×17 works.  \n5. All work: 48÷3=16 ✓ , 48÷4=12 ✓ , 48÷6=8 ✓ , 48÷8=6 ✓  \n6. 12 days (LCM of 4 and 6 = 12)  \n7. Rows of 2: 16 rows; rows of 4: 8 rows; rows of 8: 4 rows  \n8. No. 15 ÷ 4 = 3 R3 . The closest multiples of 4 are 12 and 16.  \n9. 1×28, 2×14, 4×7 (factors of 28: 1, 2, 4, 7, 14, 28)  \n10.Yes. 56 = 8 × 7. The garden needs 7 packs.  \n11. Day 15 (LCM of 3 and 5 = 15)  \nChallenge: Missing factor: 9. Full list: 1×18, 2×9, 3×6 . (Factors of 18: 1, 2, 3, 6, 9, 18)  \n4  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)","cbCaihU3V8vppWFi","https://ap.wps.com/l/cbCaihU3V8vppWFi","pdf",897575,"English","# Word Problems\n## Factors and Factor Pairs\n## Multiples and Closest Multiples\n## Prime vs Composite\n## Equal Rows and Plots\n## LCM Scheduling\n## Challenge Error Analysis","[{\"question\":\"How do you determine factor pairs for a given number in these problems?\",\"answer\":\"Find all pairs of whole numbers that multiply to the given number. The worksheet shows examples like listing factors for 24 and 28.\"},{\"question\":\"How can you tell whether one number is a multiple of another?\",\"answer\":\"Check whether the larger number is divisible by the given factor with no remainder. For example, 42 is a multiple of 6 because 42 = 6 × 7.\"},{\"question\":\"What does the LCM calculation represent in the scheduling problem?\",\"answer\":\"The LCM gives the first day both volunteers meet based on their watering intervals. The answer uses LCM(4, 6) = 12 and LCM(3, 5) = 15.\"}]","Factors - Multiples Word Problems - Answer Key | PDF",1790136106]