[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-572861-105":3,"detail-sidebar-cat-1-en-105":80,"doc-detail-572861-en":126},{"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":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","harolds-times-tables-cheat-sheet-prime-factoring-tips-for-multiplication","Harold's Times Tables Cheat Sheet - Prime factoring tips for multiplication","","Harold’s Times Tables Cheat Sheet provides quick mental-math rules and prime-factoring tips for multiplication. It lists digit-by-digit fill-in strategies (e.g., doubling, tripling, trailing-zero handling, and divisibility checks) to help determine whether results are integers and to identify factors. The sheet also includes full multiplication tables for 12×12 and 25×25, plus a mental-math grid for 12×12, supporting fast practice and verification.",{"@graph":14,"@context":72},[15,34,55],{"@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/template/","Template",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/template/paper-templates/","Paper Templates",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/template/harolds-times-tables-cheat-sheet-prime-factoring-tips-for-multiplication/572861/",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/harolds-times-tables-cheat-sheet-prime-factoring-tips-for-multiplication/572861.png","ImageObject",442,249,{"name":42,"@type":43},"Logic","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-15","2026-10-13",true,{"@type":52,"interactionType":53,"userInteractionCount":22},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"How does the cheat sheet help with prime factoring when multiplying?","Question",{"text":62,"@type":63},"It pairs each digit with factoring tips, such as checking known prime facts for certain numbers and applying divide/cut strategies while keeping only integer outcomes.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"What rules are provided for digits 1 through 12?",{"text":67,"@type":63},"Each digit includes guidance like copying/doubling/tripling, trailing-zero handling, and divisibility checks (e.g., using digit-sum logic for 9) to spot factors quickly.",{"name":69,"@type":60,"acceptedAnswer":70},"What multiplication tables are included for practice?",{"text":71,"@type":63},"The document contains a mental-math 12×12 table and full multiplication tables for 12×12 and 25×25 to support fast calculation and verification.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},572861,1792062410,{"code":4,"msg":81,"data":82},"success",[83,88,93,98,103,108,113,118,122],{"id":84,"doc_module":22,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},11,"Presentations",90,"presentations",{"id":89,"doc_module":22,"doc_module_name":25,"category_name":90,"show_sort_weight":91,"slug":92},12,"Resumes",80,"resumes",{"id":94,"doc_module":22,"doc_module_name":25,"category_name":95,"show_sort_weight":96,"slug":97},14,"Invoices",70,"invoices",{"id":99,"doc_module":22,"doc_module_name":25,"category_name":100,"show_sort_weight":101,"slug":102},15,"Posters",60,"posters",{"id":104,"doc_module":22,"doc_module_name":25,"category_name":105,"show_sort_weight":106,"slug":107},16,"Social Media",50,"social-media",{"id":109,"doc_module":22,"doc_module_name":25,"category_name":110,"show_sort_weight":111,"slug":112},17,"Forms",40,"forms",{"id":114,"doc_module":22,"doc_module_name":25,"category_name":115,"show_sort_weight":116,"slug":117},18,"Letters",30,"letters",{"id":119,"doc_module":22,"doc_module_name":25,"category_name":29,"show_sort_weight":120,"slug":121},21,5,"papers-templates",{"id":123,"doc_module":22,"doc_module_name":25,"category_name":124,"show_sort_weight":4,"slug":125},158,"General","general-158",{"code":4,"msg":81,"data":127},{"doc_id":78,"user_id":128,"nickname":42,"user_avatar":129,"doc_module":22,"category_id":119,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":22,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":135,"language":136,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":12,"update_tm":140,"read_time":26},1099513958762,"https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253","Harold’s Times Tables Cheat Sheet  \n9 February 2025  \n\n| Digit | Fill-In Tips | How to Spot | Prime Factoring Tips |\n| --- | --- | --- | --- |\n| 1 | Copy n | Same as n | See prime numbers (2,3,5,7,11,13,17,19,23,29,31,…) |\n| 2 | Double n | If the last digit is even {0, 2, 4, 6, 8} | Cut in half. Keep if the result is an integer. Factors: {2,…, 􀝉} |\n| 3 | Triple n | See 9’s Rule below | Divide by ‘3’. Keep if the result is an integer. Factors: {3,…, 􀝉} |\n| 4 | Double n twice | If the last digit is even, then a candidate | Cut in half twice. Keep if the result is an integer. Factors: {4,…, 􀝉} → {2, 2,…, 􀝉} |\n| 5 | Add a trailing ‘0’ to n, then cut in half | If the last digit is a ‘0’ or ‘5’ | See 10’s Rule below if trailing ‘0’.\u003Cbr>Divide by ‘5’ if trailing ‘5’.\u003Cbr>Factors: {5,…, 􀝉} |\n| 6 | Triple n, then Double | 6, 12, 18, 24, 30, 36, 42, 48, 54, 60,… | Cut in half, then divide by ‘3’.\u003Cbr>Keep if the result is an integer.\u003Cbr>Factors: {6,…, 􀝉} → {2, 3,…, 􀝉} |\n| 7 | Memorize | Hardest | Divide by ‘7’ after trying all other factoring tips. Factors: {7,…, 􀝉} |\n| 8 | Double n 3 times | If the last digit is even, then a candidate | Cut in half three times.\u003Cbr>Keep if the result is an integer.\u003Cbr>Factors: {8,…, 􀝉} → {2, 2, 2,…, 􀝉} |\n| 9 | If n ≤ 10, then_ (n-1)  (9-(n-1))_ | Digits add up to ‘9’ or multiples of ‘9’\u003Cbr>(9m) | Add up all digits, then divide by ‘9’.\u003Cbr>If the result is an integer, then ‘9’ is a factor. Factors: {9,…, 􀝉} → {3, 3,…, 􀝉} |\n| 10 | Add a trailing ‘0’ to n | If the last digit is a ‘0’ | Drop trailing zero to get the factors {2, 5} . Factors: {10,…, 􀝉} → {2, 5,…, 􀝉} |\n| 11 | If n ≤ 9, then\u003Cbr>_n_n_ | You see double-digits | Divide by ‘11’. Keep if the result is an integer. Factors: {11,…, 􀝉} |\n| 12 | 12 · 12 = 144 | Is even and large | Cut in half twice, then divide by ‘3’.\u003Cbr>Keep if the result is an integer.\u003Cbr>Factors: {12,…, 􀝉} → {2, 2, 3,…, 􀝉} |\n\nMental Math  \nMultiplication Table – 12 ⨯ 12  \n\n| ⨯ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |\n| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 |\n| 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 |\n| 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 |\n| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 |\n| 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72 |\n| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 |\n| 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 |\n| 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 |\n| 10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 |\n| 11 | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 121 | 132 |\n| 12 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 | 132 | 144 |\n\nMultiplication Table – 12 ⨯ 12  \n\n| ⨯ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 1 |  |  |  |  |  |  |  |  |  |  |  |  |\n| 2 |  |  |  |  |  |  |  |  |  |  |  |  |\n| 3 |  |  |  |  |  |  |  |  |  |  |  |  |\n| 4 |  |  |  |  |  |  |  |  |  |  |  |  |\n| 5 |  |  |  |  |  |  |  |  |  |  |  |  |\n| 6 |  |  |  |  |  |  |  |  |  |  |  |  |\n| 7 |  |  |  |  |  |  |  |  |  |  |  |  |\n| 8 |  |  |  |  |  |  |  |  |  |  |  |  |\n| 9 |  |  |  |  |  |  |  |  |  |  |  |  |\n| 10 |  |  |  |  |  |  |  |  |  |  |  |  |\n| 11 |  |  |  |  |  |  |  |  |  |  |  |  |\n| 12 |  |  |  |  |  |  |  |  |  |  |  |  |\n\nMultiplication Table – 25 ⨯ 25  \n\n| ⨯ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 |\n| 2 | 2 | 4 | 6 ","cbCaibpwFCrdundc","https://ap.wps.com/l/cbCaibpwFCrdundc","pdf",451684,6,"English","# Prime factoring and digit rules\n## Fill-in tips and divisibility checks\n# Mental math multiplication tables\n## 12 × 12\n## 25 × 25","[{\"question\":\"How does the cheat sheet help with prime factoring when multiplying?\",\"answer\":\"It pairs each digit with factoring tips, such as checking known prime facts for certain numbers and applying divide/cut strategies while keeping only integer outcomes.\"},{\"question\":\"What rules are provided for digits 1 through 12?\",\"answer\":\"Each digit includes guidance like copying/doubling/tripling, trailing-zero handling, and divisibility checks (e.g., using digit-sum logic for 9) to spot factors quickly.\"},{\"question\":\"What multiplication tables are included for practice?\",\"answer\":\"The document contains a mental-math 12×12 table and full multiplication tables for 12×12 and 25×25 to support fast calculation and verification.\"}]","Harold's Times Tables Cheat Sheet - Prime factoring tips for multiplication | PDF",1791929730]