{"id":491,"date":"2022-04-13T05:21:04","date_gmt":"2022-04-13T05:21:04","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=491"},"modified":"2025-02-23T06:37:33","modified_gmt":"2025-02-23T06:37:33","slug":"y-1-hcf-of-monomials","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/y-1-hcf-of-monomials\/","title":{"rendered":"Y.1 HCF of monomials"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>HCF of monomials<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-4d4696560822e7cb72ec4be90d4370b1\" style=\"color:#74008b\">Key Notes:<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-fe99173d877ae78bbc11da14667838d8\" style=\"color:#000060\"><strong>Definition of Monomials:<\/strong> <\/p>\n\n\n\n<p class=\"has-large-font-size\">Monomials are algebraic expressions with one term. Examples include 3x, -5y\u00b2, and 4ab.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-62269114b6f4a911d767f7f59b2013d6\" style=\"color:#000060\"><strong>Understanding HCF (Highest Common Factor):<\/strong> <\/p>\n\n\n\n<p class=\"has-large-font-size\">HCF of monomials involves finding the highest common factor of the numerical coefficients and variables&#8217; highest powers in the monomials.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-c2130662e0b7bb646f3efa41b9626578\" style=\"color:#000060\"><strong>Steps to Find HCF of Monomials:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Step 1:<\/strong> Identify the numerical coefficients of the monomials.<\/li>\n\n\n\n<li><strong>Step 2:<\/strong> Identify the variables and their highest powers in each monomial.<\/li>\n\n\n\n<li><strong>Step 3:<\/strong> Determine the lowest powers of the variables common to all monomials.<\/li>\n\n\n\n<li><strong>Step 4:<\/strong> Multiply the HCF of numerical coefficients by the common variables raised to their lowest powers.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Example:<\/strong> Find the HCF of 6xy\u00b2 and 15x\u00b2y\u00b3.<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Numerical coefficients: HCF of 6 and 15 is 3.<\/li>\n\n\n\n<li>Variables: HCF of x (power 1) and y (power 2) is xy\u00b2.<\/li>\n\n\n\n<li>HCF of monomials = 3xy\u00b2.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-99ebe2638e306f91b8efbb4971d79612\" style=\"color:#000060\"><strong>Application in Simplification:<\/strong> <\/p>\n\n\n\n<p class=\"has-large-font-size\">HCF of monomials is crucial in simplifying algebraic expressions and solving equations involving variables.<\/p>\n\n\n\n<p class=\"has-large-font-size\">To&nbsp;find the highest common factor (HCF) of two or more monomials, find the prime factorisation of each monomial, identify the common factors, and multiply them&nbsp;together.<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#540202\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-6ac82963806d3ab718a3b270b9adc8e6\" style=\"color:#b00012\">\ud83c\udfda\ufe0f<strong>Find&nbsp;the highest common&nbsp;factor.<\/strong><\/p>\n\n\n\n<p>9a<sup>3<\/sup>,&nbsp;6a<sup>3<\/sup><\/p>\n\n\n\n<p><em>Write&nbsp;your answer as a constant times a product of single variables raised to&nbsp;exponents.<\/em>&#8212;&#8212;-<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-f236258255376a0b69027cbff6bb83b7\">First,&nbsp;factorise each monomial and find the common&nbsp;factors.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-e99576319b4bf1acc583f0339e877541\">9a<sup>3<\/sup>=<strong>3<\/strong> . 3 . a . a . a<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-34fe276e93b19b22beeb66487d69eb54\">6a<sup>3<\/sup>=2 . <strong>3<\/strong> . a . a . a<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-bc4144e5bef998c35dfc267415cbb34c\">The&nbsp;common factors are&nbsp;3,&nbsp;a,&nbsp;a&nbsp;and&nbsp;a.&nbsp;Multiply them to find the highest common&nbsp;factor.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-ccf93e25723ce94b3c1b793cc9684cad\">3 . a . a . a=3a<sup>3<\/sup><\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-c3653bdd2df972e93bbad65d3bd9f368\">The&nbsp;highest common factor is&nbsp;3a<sup>3<\/sup>.<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#045503\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-3fb49e5e04a128842248d06605da6275\" style=\"color:#b00012\">\ud83c\udfda\ufe0f <strong>Find&nbsp;the highest common&nbsp;factor.<\/strong><\/p>\n\n\n\n<p>6w,&nbsp;2w<sup>3<\/sup><\/p>\n\n\n\n<p><em>Write&nbsp;your answer as a constant times a product of single variables raised to&nbsp;exponents.<\/em>&#8212;&#8212;-<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-f236258255376a0b69027cbff6bb83b7\">First,&nbsp;factorise each monomial and find the common&nbsp;factors.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-5da96a73abbdfa6ef648a99f8547b61f\">6w=<strong>2<\/strong> . 3 . w<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-8f724c5e1fc795dce695c9d29324d7b1\">2w<sup>3<\/sup>=<strong>2<\/strong> . w . w . w<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-42ea70ac48a36319f5bc1aa61580ab52\">The&nbsp;common factors are&nbsp;2&nbsp;and&nbsp;w.&nbsp;Multiply them to find the highest common&nbsp;factor.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-bab5b05560e2400173b543602609ef8a\">2 . w=2w<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-3a2bc6f23082fbdeedccbaa25e46523c\">The&nbsp;highest common factor is&nbsp;2w.<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#01365e\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-3fb49e5e04a128842248d06605da6275\" style=\"color:#b00012\">\ud83c\udfda\ufe0f <strong>Find&nbsp;the highest common&nbsp;factor.<\/strong><\/p>\n\n\n\n<p>2y<sup>2<\/sup>,&nbsp;10y<\/p>\n\n\n\n<p><em>Write&nbsp;your answer as a constant times a product of single variables raised to&nbsp;exponents.<\/em>&#8212;&#8212;<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-f236258255376a0b69027cbff6bb83b7\">First,&nbsp;factorise each monomial and find the common&nbsp;factors.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-775dafdfd0a9a49d58d28767a593816f\">2y<sup>2<\/sup>=<strong>2<\/strong> . y . y<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-e695f545c5ee70d687ab19838c12f562\">10y=<strong>2<\/strong> . 5 . y<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-cd117d794690c2657c67dc90d7335d7b\">The&nbsp;common factors are&nbsp;2&nbsp;and&nbsp;y.&nbsp;Multiply them to find the highest common&nbsp;factor.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-c02abfc52f5cc672d00ae330f8ed9081\">2 . y=2y<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-5bca71908a47cbf830399ac91986cbdb\">The&nbsp;highest common factor is&nbsp;2y.<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/86337\/836\/613\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-171.png\" alt=\"\" class=\"wp-image-9042\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-171.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-171-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-171-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/86172\/976\/902\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-176.png\" alt=\"\" class=\"wp-image-9043\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-176.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-176-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-176-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>HCF of monomials Key Notes: Definition of Monomials: Monomials are algebraic expressions with one term. Examples include 3x, -5y\u00b2, and 4ab. Understanding HCF (Highest Common Factor): HCF of monomials involves finding the highest common factor of the numerical coefficients and variables&#8217; highest powers in the monomials. Steps to Find HCF of Monomials: Example: Find the<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/y-1-hcf-of-monomials\/\">Continue reading <span class=\"screen-reader-text\">&#8220;Y.1 HCF of monomials&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-491","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"_links":{"self":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/491","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=491"}],"version-history":[{"count":18,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/491\/revisions"}],"predecessor-version":[{"id":19940,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/491\/revisions\/19940"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=491"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}