{"id":501872,"date":"2023-04-19T07:18:33","date_gmt":"2023-04-19T01:48:33","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/if-the-hcf-of-657-and-963-is-expressible-in-the-form-657x963x-15-find-x\/"},"modified":"2025-06-20T14:27:16","modified_gmt":"2025-06-20T08:57:16","slug":"if-the-hcf-of-657-and-963-is-expressible-in-the-form-657x963x-15-find-x","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/if-the-hcf-of-657-and-963-is-expressible-in-the-form-657x96\/","title":{"rendered":"If the HCF of 657 and 963 is expressible in the form 657x+963\u00d7(-15), find x."},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"If the HCF of 657 and 963 is expressible in the form 657x+963\u00d7(-15), find x.","custom_permalink":"question\/mathematics\/if-the-hcf-of-657-and-963-is-expressible-in-the-form-657x96\/"},"categories":[],"acf":{"question":"

If the HCF of 657 and 963 is expressible in the form <\/span>657<\/mn>x<\/mi>+<\/mo>963<\/mn>\u00d7<\/mo>(<\/mo>-<\/mo>15<\/mn>)<\/mo><\/math>, find x.<\/span><\/p>

<\/p>

<\/p><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\"><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\">","options":[{"option":"10","correct":false},{"option":"15","correct":false},{"option":"20","correct":false},{"option":"22 <\/span>","correct":true}],"solution":"The given numbers are 657 and 963.<\/span>
Euclid's Division Lemma<\/span> <\/span>states that, if two positive integers \u201ca\u201d and \u201cb\u201d, then there exists unique integers \u201cq\u201d and \u201cr\u201d such that which satisfies the condition:<\/span>
a<\/mi>=<\/mo>bq<\/mi>+<\/mo>r<\/mi><\/math> where <\/span>0<\/mn>\u2264<\/mo>r<\/mi>\u2264<\/mo>b<\/mi><\/math>
Calculation of HCF using Euclid\u2019s division algorithm is as follows:<\/span>
963<\/mn>=<\/mo>657<\/mn>\u00d7<\/mo>1<\/mn>+<\/mo>306<\/mn><\/math>
\u21d2<\/mo>657<\/mn>=<\/mo>306<\/mn>\u00d7<\/mo>2<\/mn>+<\/mo>45<\/mn><\/math>
\u21d2<\/mo>306<\/mn>=<\/mo>45<\/mn>\u00d7<\/mo>6<\/mn>+<\/mo>36<\/mn><\/math>
\u21d2<\/mo>45<\/mn>=<\/mo>36<\/mn>\u00d7<\/mo>1<\/mn>+<\/mo>9<\/mn><\/math>
\u21d2<\/mo>36<\/mn>=<\/mo>9<\/mn>\u00d7<\/mo>4<\/mn>+<\/mo>0<\/mn><\/math>
\u21d2<\/mo>HCF<\/mi>(<\/mo>657<\/mn>,<\/mo>963<\/mn>)<\/mo>=<\/mo>9<\/mn><\/math>
Calculate x.<\/span>
HCF<\/mi>=<\/mo>657<\/mn>x<\/mi>+<\/mo>963<\/mn>\u00d7<\/mo>(<\/mo>-<\/mo>15<\/mn>)<\/mo><\/math>
9<\/mn>=<\/mo>657<\/mn>x<\/mi>+<\/mo>963<\/mn>\u00d7<\/mo>(<\/mo>-<\/mo>15<\/mn>)<\/mo><\/math>
\u21d2<\/mo>9<\/mn>=<\/mo>657<\/mn>x<\/mi>-<\/mo>14445<\/mn><\/math>
\u21d2<\/mo>657<\/mn>x<\/mi>=<\/mo>14445<\/mn>+<\/mo>9<\/mn><\/math>
\u21d2<\/mo>657<\/mn>x<\/mi>=<\/mo>14454<\/mn><\/math>
\u21d2<\/mo>x<\/mi>=<\/mo>14454<\/mn><\/mrow>657<\/mn><\/mrow><\/mfrac><\/math>
\u21d2<\/mo>x<\/mi>=<\/mo>22<\/mn><\/math>
Therefore, if the HCF of 657 and 963 is expressible in the form <\/span>657<\/mn>x<\/mi>+<\/mo>963<\/mn>\u00d7<\/mo>(<\/mo>-<\/mo>15<\/mn>)<\/mo><\/math> then the value of x is 22.<\/span>
Hence, option 4 is correct.<\/span>
 <\/span>","subject":"Mathematics"},"yoast_head":"\nIf the HCF of 657 and 963 is expressible in the form 657x+963\u00d7(-15), find x. - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"If the HCF of 657 and 963 is expressible in the form 657x+963\u00d7(-15), find x.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/if-the-hcf-of-657-and-963-is-expressible-in-the-form-657x96\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If the HCF of 657 and 963 is expressible in the form 657x+963\u00d7(-15), find x. - Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"og:description\" content=\"If the HCF of 657 and 963 is expressible in the form 657x+963\u00d7(-15), find x.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/if-the-hcf-of-657-and-963-is-expressible-in-the-form-657x96\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:modified_time\" content=\"2025-06-20T08:57:16+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1008\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"If the HCF of 657 and 963 is expressible in the form 657x+963\u00d7(-15), find x. - 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