[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-360581-105":59,"doc-detail-360581-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-word-problems","Factors & Multiples Word Problems","","A K-12 math worksheet focused on factors and multiples through a set of practical word problems. Students solve for factor pairs, determine whether one number is a multiple of another, and find common arrival days using LCM. Problems include dividing parking spaces or trees into equal sections, grouping windows, placing lamps and benches across streets or paths, and identifying prime versus composite numbers. An answer key and a challenge error-analysis question on missing factors are included.",{"@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-word-problems/360581/",{"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-word-problems/360581.png","ImageObject",300,407,{"name":92,"@type":93},"Melati","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-27","2026-09-23",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you find all factor pairs for a number in these problems?","Question",{"text":113,"@type":114},"Find every pair of whole numbers whose product equals the target number. For example, for 30 you list pairs like 1×30, 2×15, 3×10, and 5×6.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How can you tell whether one number is a multiple of another?",{"text":118,"@type":114},"Divide the larger claim number by the base number and check that the division has no remainder. If it divides evenly, it is a multiple, such as 36 being a multiple of 4 because 36 = 4×9.",{"name":120,"@type":111,"acceptedAnswer":121},"What method is used to find when two events occur on the same day?",{"text":122,"@type":114},"Compute the LCM of the two cycle lengths and use it to identify the first common day. For example, LCM(6, 9) = 18 days for simultaneous arrival.","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},360581,1790448520,{"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},962085570644,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","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 city block has 30 parking spaces to divide into equal sections with none left over. List all the ways to divide them. (Hint: find all factor pairs of 30 . )  \nAnswer:   2.  \nA bus comes every 4 minutes. Is 36 a multiple of 4?  \nExplain how you know, then list 3 more multiples of 4 greater than 36.  \nAnswer:   3.  \nA planner wants to plant 45 trees in equal rows along a street.  \nWhich row sizes work with no trees left over: 4, 5, 6, 7, or 9?  \nAnswer:   4.  \nIs 13 prime or composite? A builder wants 13 windows in identical groups.  \nExplain why only one grouping is possible.  \nAnswer:   5.  \nA city has 60 lamp posts to place equally on its streets.  \nDo 4, 5, 6, and 10 all work as the number of streets? Show your work for each.  \nAnswer:   6.  \nStreet sweepers come every 6 days. Trash trucks come every 9 days.  \nHow many days until both arrive on the same day? (Find the LCM of 6 and 9. )  \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 40 park benches to place equally on 2, 4, 5, or 8 paths. How many benches go on each path in each arrangement?  \nAnswer:   8.  \nA city engineer says 21 is a multiple of 6. Is she correct?  \nExplain your reasoning and name the multiples of 6 closest to 21.  \nAnswer:   9.  \nA city block has 42 apartments to group into equal floors. List all factor pairs of 42.  \nAnswer:   10.  \nNew streetlights come in boxes of 9. The city needs exactly 72 lights. Is 72 a multiple of 9? How many boxes are needed?  \nAnswer:   11.  \nA mail carrier delivers every 2 days. A recycling truck comes every 7 days. What is the first day both arrive on the same day?  \nAnswer:    \nChallenge Problem – Error Analysis  \nA student solved this problem:  \nA student says the factors of 24 are: 1, 2, 3, 4, 6, 8, and 24.  \nA city planner uses this list to arrange 24 trees equally. One factor is missing.  \nThe student is missing one factor. Identify the missing factor.  \nFind the missing factor, explain what factor pair it completes, and list all factor pairs of 24.  \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)  \nANSWER KEY  \n1. 1×30, 2×15, 3×10, 5×6 (factors of 30: 1, 2, 3, 5, 6, 10, 15, 30)  \n2. Yes. 36 = 4 × 9. Next multiples: 40, 44, 48  \n3. 5 and 9 (45 = 5×9 and 45 = 9×5; not divisible by 4, 6, or 7)  \n4. Prime. 13 has no factors other than 1 and 13. Only 1×13 works.  \n5. All work: 60÷4=15 ✓ , 60÷5=12 ✓ , 60÷6=10 ✓ , 60÷10=6 ✓  \n6. 18 days (LCM of 6 and 9 = 18)  \n7. 2 paths: 20; 4 paths: 10; 5 paths: 8; 8 paths: 5  \n8. No. 21 ÷ 6 = 3 R3 . The closest multiples of 6 are 18 and 24.  \n9. 1×42, 2×21, 3×14, 6×7 (factors of 42: 1, 2, 3, 6, 7, 14, 21, 42)  \n10.Yes. 72 = 9 × 8. The city needs 8 boxes.  \n11. Day 14 (LCM of 2 and 7 = 14)  \nChallenge: Missing factor: 12. Full list: 1×24, 2×12, 3×8, 4×6 . (Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24)  \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","cbCail47ChB5176Y","https://ap.wps.com/l/cbCail47ChB5176Y","pdf",545494,"English","# Factors and Multiples Word Problems\n## Directions\n## Problems\n## Challenge Problem – Error Analysis\n## Answer Key","[{\"question\":\"How do you find all factor pairs for a number in these problems?\",\"answer\":\"Find every pair of whole numbers whose product equals the target number. For example, for 30 you list pairs like 1×30, 2×15, 3×10, and 5×6.\"},{\"question\":\"How can you tell whether one number is a multiple of another?\",\"answer\":\"Divide the larger claim number by the base number and check that the division has no remainder. If it divides evenly, it is a multiple, such as 36 being a multiple of 4 because 36 = 4×9.\"},{\"question\":\"What method is used to find when two events occur on the same day?\",\"answer\":\"Compute the LCM of the two cycle lengths and use it to identify the first common day. For example, LCM(6, 9) = 18 days for simultaneous arrival.\"}]","Factors & Multiples Word Problems | PDF",1790140591]