{"id":1790,"date":"2025-05-02T23:21:57","date_gmt":"2025-05-02T17:51:57","guid":{"rendered":"https:\/\/leverageedu.com\/questions-answers\/?p=1790"},"modified":"2025-05-02T23:22:27","modified_gmt":"2025-05-02T17:52:27","slug":"how-many-numbers-of-two-digit-are-divisible-by-3-class-10-maths-cbse","status":"publish","type":"post","link":"https:\/\/leverageedu.com\/questions-answers\/how-many-numbers-of-two-digit-are-divisible-by-3-class-10-maths-cbse\/","title":{"rendered":"How Many Numbers of Two Digit are Divisible by 3?"},"content":{"rendered":"\n<p><strong>Answer:<\/strong> There are 30 two-digit numbers that are divisible by 3.<\/p>\n\n\n\n<h2 id=\"step-by-step-solution\" class=\"wp-block-heading\">Step-by-Step Solution<\/h2>\n\n\n\n<p>We are asked to find how many two-digit numbers are divisible by 3.<\/p>\n\n\n\n<p><strong>Step 1: Identify the range of two-digit numbers<\/strong><\/p>\n\n\n\n<p>Two-digit numbers start from 10 and go up to 99.<\/p>\n\n\n\n<p>So, we are looking for all numbers between 10 and 99 that are divisible by 3.<\/p>\n\n\n\n<p><strong>Step 2: Use the concept of Arithmetic Progression (A.P.)<\/strong><\/p>\n\n\n\n<p>The numbers divisible by 3 in this range form an arithmetic progression:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The first two-digit number divisible by 3 is 12<br>(Since 3 \u00d7 4 = 12 and 12 is the first two-digit multiple of 3)<\/li>\n\n\n\n<li>The last two-digit number divisible by 3 is 99<br>(Because 3 \u00d7 33 = 99, which is the last two-digit multiple of 3)<\/li>\n<\/ul>\n\n\n\n<p>Now, we have an A.P.: 12, 15, 18, \u2026, 99\u00a0<\/p>\n\n\n\n<p>Here,<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>First term (<strong>a<\/strong>) = 12<\/li>\n\n\n\n<li>Last term (<strong>l<\/strong>) = 99<\/li>\n\n\n\n<li>Common difference (<strong>d<\/strong>) = 3<\/li>\n<\/ul>\n\n\n\n<p><strong>Step 3: Use the A.P. formula to find the number of terms<\/strong><\/p>\n\n\n\n<p>The formula to find the number of terms (<strong>n<\/strong>) in an A.P. is:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh7-rt.googleusercontent.com\/docsz\/AD_4nXcFk7oRAUkzsAHdCAMxyZCc1dR8fgHkQOt7hNlqIXkXMqR9hI_ZE3NxK1FlsEGFQ9N3gV8n5vAJ9xgLNDWoHd2hHZdw7M5QRoQZ9iVhjyNgEFWY9mHlMey-lSrVu5bJWA4gPkMQ?key=tCIOltARGgUg3Kske-GYNG7u\" alt=\"\" \/><\/figure>\n\n\n\n<p>Substitute the values:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh7-rt.googleusercontent.com\/docsz\/AD_4nXePzlOFBpAclcgEq9adp3jlGFvLMiAWSNHPyQIdQCEcG71geB0q3mNLM05dSgdvoaRTo-rIOSKeW2QJgCg1cfIXXvKvoEgh7fV6hsmBl09XNNjfrav9fEN_lLlhRV3VH113reI7og?key=tCIOltARGgUg3Kske-GYNG7u\" alt=\"\" \/><\/figure>\n\n\n\n<p><strong>\u2705 Final Answer:<\/strong><\/p>\n\n\n\n<p>There are 30 two-digit numbers divisible by 3.<\/p>\n\n\n\n<h3 id=\"quick-tip-for-class-10-students\" class=\"wp-block-heading\">Quick Tip for Class 10 Students<\/h3>\n\n\n\n<p>Instead of checking each number individually, you can apply the A.P. formula anytime you need to count numbers divisible by a fixed number within a range. It\u2019s a major time-saver, especially in competitive exams or board tests!<\/p>\n\n\n\n<p class=\"has-text-align-center has-vivid-red-color has-text-color has-link-color has-medium-font-size wp-elements-1c63c82f21fc811736e69d889c25acdd\"><strong>Common Doubts in Maths<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><a href=\"https:\/\/leverageedu.com\/questions-answers\/number-of-prime-between-1-to-100-is\/\"><strong>Number of Prime Between 1 to 100 is<\/strong><\/a><\/td><td><a href=\"https:\/\/leverageedu.com\/questions-answers\/how-many-seconds-in-an-hour-are-there\/\"><strong>How Many Seconds in an Hour Are There?<\/strong><\/a><\/td><\/tr><tr><td><a href=\"https:\/\/leverageedu.com\/questions-answers\/correct-the-following-1m-1000-cm\/\"><strong>Correct the following: 1 m = 1000 cm.<\/strong><\/a><\/td><td><a href=\"https:\/\/leverageedu.com\/questions-answers\/how-many-ten-lakhs-are-in-one-crore\/\"><strong>How many ten lakhs are in one crore?<\/strong><\/a><\/td><\/tr><tr><td><a href=\"https:\/\/leverageedu.com\/questions-answers\/what-is-the-smallest-3-digit-number-with-unique-digits\/\"><strong>What is the Smallest 3-Digit Number with Unique Digits?<\/strong><\/a><\/td><td><a href=\"https:\/\/leverageedu.com\/questions-answers\/difference-of-the-smallest-6-digit-number-and-the-greatest-4-digit-number-is\/\"><strong>Difference between the Smallest 6-digit number and the Greatest 4 Digit Number is<\/strong><\/a><\/td><\/tr><tr><td><a href=\"https:\/\/leverageedu.com\/questions-answers\/find-the-value-of-this-expression-sin-30cos-60-sin-60cos-30\/\"><strong>Find the Value of this Expression: sin 30Cos60+sin 60cos30\u00a0<\/strong><\/a><\/td><td><a href=\"https:\/\/leverageedu.com\/questions-answers\/convert-200-million-dollars-in-rupees\/\"><strong>Convert 200 Million Dollars in Rupees<\/strong><\/a><\/td><\/tr><tr><td><a href=\"https:\/\/leverageedu.com\/questions-answers\/list-of-coprime-numbers-from-1-to-100\/\"><strong>List of coprime numbers from 1 to 100<\/strong><\/a><\/td><td><a href=\"https:\/\/leverageedu.com\/questions-answers\/degree-of-the-zero-polynomial-is\/\"><strong>Degree of the Zero Polynomial is<\/strong><\/a><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"Answer: There are 30 two-digit numbers that are divisible by 3. Step-by-Step Solution We are asked to find&hellip;\n","protected":false},"author":90,"featured_media":1792,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"editor_notices":[],"footnotes":""},"categories":[3],"tags":[],"class_list":{"0":"post-1790","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-math"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>How Many Numbers of Two Digit are Divisible by 3?<\/title>\n<meta name=\"description\" content=\"How Many Numbers of Two Digit are Divisible by 3? 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There are 30 two-digit numbers in total that are divisible by 3.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/leverageedu.com\/questions-answers\/how-many-numbers-of-two-digit-are-divisible-by-3-class-10-maths-cbse\/","og_locale":"en_US","og_type":"article","og_title":"How Many Numbers of Two Digit are Divisible by 3?","og_description":"How Many Numbers of Two Digit are Divisible by 3? There are 30 two-digit numbers in total that are divisible by 3.","og_url":"https:\/\/leverageedu.com\/questions-answers\/how-many-numbers-of-two-digit-are-divisible-by-3-class-10-maths-cbse\/","og_site_name":"Questions &amp; Answers","article_published_time":"2025-05-02T17:51:57+00:00","article_modified_time":"2025-05-02T17:52:27+00:00","og_image":[{"width":1024,"height":640,"url":"https:\/\/blogassets.leverageedu.com\/media\/uploads\/sites\/5\/2025\/05\/02232126\/How-Many-Numbers-of-Two-Digit-are-Divisible-by-3.jpg","type":"image\/jpeg"}],"author":"Harshita","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Harshita","Est. reading time":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/leverageedu.com\/questions-answers\/how-many-numbers-of-two-digit-are-divisible-by-3-class-10-maths-cbse\/#article","isPartOf":{"@id":"https:\/\/leverageedu.com\/questions-answers\/how-many-numbers-of-two-digit-are-divisible-by-3-class-10-maths-cbse\/"},"author":{"name":"Harshita","@id":"https:\/\/leverageedu.com\/questions-answers\/#\/schema\/person\/b7c61d659576ff5b72293043173c8640"},"headline":"How Many Numbers of Two Digit are Divisible by 3?","datePublished":"2025-05-02T17:51:57+00:00","dateModified":"2025-05-02T17:52:27+00:00","mainEntityOfPage":{"@id":"https:\/\/leverageedu.com\/questions-answers\/how-many-numbers-of-two-digit-are-divisible-by-3-class-10-maths-cbse\/"},"wordCount":288,"commentCount":0,"image":{"@id":"https:\/\/leverageedu.com\/questions-answers\/how-many-numbers-of-two-digit-are-divisible-by-3-class-10-maths-cbse\/#primaryimage"},"thumbnailUrl":"https:\/\/blogassets.leverageedu.com\/media\/uploads\/sites\/5\/2025\/05\/02232126\/How-Many-Numbers-of-Two-Digit-are-Divisible-by-3.jpg","articleSection":["Maths"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/leverageedu.com\/questions-answers\/how-many-numbers-of-two-digit-are-divisible-by-3-class-10-maths-cbse\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/leverageedu.com\/questions-answers\/how-many-numbers-of-two-digit-are-divisible-by-3-class-10-maths-cbse\/","url":"https:\/\/leverageedu.com\/questions-answers\/how-many-numbers-of-two-digit-are-divisible-by-3-class-10-maths-cbse\/","name":"How Many Numbers of Two Digit are Divisible by 3?","isPartOf":{"@id":"https:\/\/leverageedu.com\/questions-answers\/#website"},"primaryImageOfPage":{"@id":"https:\/\/leverageedu.com\/questions-answers\/how-many-numbers-of-two-digit-are-divisible-by-3-class-10-maths-cbse\/#primaryimage"},"image":{"@id":"https:\/\/leverageedu.com\/questions-answers\/how-many-numbers-of-two-digit-are-divisible-by-3-class-10-maths-cbse\/#primaryimage"},"thumbnailUrl":"https:\/\/blogassets.leverageedu.com\/media\/uploads\/sites\/5\/2025\/05\/02232126\/How-Many-Numbers-of-Two-Digit-are-Divisible-by-3.jpg","datePublished":"2025-05-02T17:51:57+00:00","dateModified":"2025-05-02T17:52:27+00:00","author":{"@id":"https:\/\/leverageedu.com\/questions-answers\/#\/schema\/person\/b7c61d659576ff5b72293043173c8640"},"description":"How Many Numbers of Two Digit are Divisible by 3? 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