{"id":3646,"date":"2026-03-21T02:15:37","date_gmt":"2026-03-21T02:15:37","guid":{"rendered":"https:\/\/npk1169-001-site1.mtempurl.com\/?p=3646"},"modified":"2026-04-19T11:21:31","modified_gmt":"2026-04-19T11:21:31","slug":"the-pulveriser-kuttaka","status":"publish","type":"post","link":"https:\/\/www.bharatwisdom.com\/hi\/mathematics\/the-pulveriser-kuttaka\/","title":{"rendered":"\u092a\u0941\u0932\u094d\u0935\u0930\u093e\u0907\u091c\u093c\u0930 (\u0915\u0941\u091f\u094d\u091f\u0915) - \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u092a\u0940\u0938\u0928\u093e"},"content":{"rendered":"<div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 fusion-flex-container nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1279.2px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-0 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:0px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-text fusion-text-1\"><p id=\"p-rc_2c7e7ac57808f84c-417\" data-path-to-node=\"67\"><span data-path-to-node=\"67,0\"><b data-path-to-node=\"67,0\" data-index-in-node=\"0\">\u0905\u0935\u0927\u093e\u0930\u0923\u093e<\/b> <\/span><span data-path-to-node=\"67,2\"><span class=\"citation-1614\">\u2018&#039;\u0915\u0941\u091f\u094d\u091f\u0915\u093e&#039; \u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u0948 \u0915\u093f\u0938\u0940 \u091a\u0940\u091c \u0915\u094b \u091b\u094b\u091f\u0947-\u091b\u094b\u091f\u0947 \u091f\u0941\u0915\u0921\u093c\u094b\u0902 \u092e\u0947\u0902 \u0924\u094b\u0921\u093c\u0928\u093e \u092f\u093e \u091a\u0915\u0928\u093e\u091a\u0942\u0930 \u0915\u0930\u0928\u093e\u0964<\/span><\/span><span data-path-to-node=\"67,4\">. <\/span><span data-path-to-node=\"67,6\"><span class=\"citation-1613\">\u092f\u0939 \u0930\u0948\u0916\u093f\u0915 \u0905\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0940 \u090f\u0915 \u0935\u093f\u0927\u093f \u0939\u0948, \u091c\u0948\u0938\u0947 \u0915\u093f <\/span><span class=\"math-inline\" data-math=\"ax + c = by\" data-index-in-node=\"66\">ax + c = by<\/span><span class=\"citation-1613\">\u00a0\u0917\u0923\u093f\u0924 \u092e\u0947\u0902<\/span><\/span><span data-path-to-node=\"67,8\">. <\/span><span data-path-to-node=\"67,10\"><span class=\"citation-1612\">\u0907\u0938\u092e\u0947\u0902 \u0939\u0932 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0928\u0947 \u0924\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u091b\u094b\u091f\u0947 \u0936\u0947\u0937\u092b\u0932\u094b\u0902 \u092e\u0947\u0902 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0928\u093e \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"67,12\">.<\/span><\/p>\n<p id=\"p-rc_2c7e7ac57808f84c-418\" data-path-to-node=\"68\"><span data-path-to-node=\"68,0\"><b data-path-to-node=\"68,0\" data-index-in-node=\"0\">\u0915\u0939\u093e\u0928\u0940<\/b> <\/span><span data-path-to-node=\"68,2\"><span class=\"citation-1611\">\u092d\u093e\u0930\u0924\u0940\u092f \u0916\u0917\u094b\u0932\u0935\u093f\u0926\u094b\u0902 \u0915\u0947 \u0938\u093e\u092e\u0928\u0947 \u090f\u0915 \u0938\u092e\u0938\u094d\u092f\u093e \u0925\u0940: \u0932\u093e\u0916\u094b\u0902 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 \u092c\u093e\u0926 \u0917\u094d\u0930\u0939\u094b\u0902 \u0915\u0947 \u090f\u0915 \u0938\u0940\u0927 \u092e\u0947\u0902 \u0906\u0928\u0947 \u0915\u093e \u0938\u091f\u0940\u0915 \u0938\u092e\u092f \u0915\u0948\u0938\u0947 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u090f?<\/span><\/span><span data-path-to-node=\"68,4\">? <\/span><span data-path-to-node=\"68,6\"><span class=\"citation-1610\">\u0907\u0938\u0947 \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0906\u0930\u094d\u092f\u092d\u091f\u094d\u091f \u0928\u0947 \u0906\u0935\u093f\u0937\u094d\u0915\u093e\u0930 \u0915\u093f\u092f\u093e <\/span><i data-path-to-node=\"68,6\" data-index-in-node=\"36\"><span class=\"citation-1610\">\u0915\u0942\u091f\u091f\u0915<\/span><\/i><span class=\"citation-1610\">, \u092f\u093e \u092b\u093f\u0930 &quot;\u0926 \u092a\u0932\u094d\u0935\u0930\u093e\u0907\u091c\u093c\u0930&quot;\u201c<\/span><\/span><span data-path-to-node=\"68,8\">. <\/span><span data-path-to-node=\"68,10\"><span class=\"citation-1609\">\u0935\u0939 \u0917\u0923\u093f\u0924 \u0915\u094b \u0905\u0928\u093e\u091c \u092a\u0940\u0938\u0928\u0947 \u0935\u093e\u0932\u0940 \u091a\u0915\u094d\u0915\u0940 \u0915\u0940 \u0924\u0930\u0939 \u092e\u093e\u0928\u0924\u0947 \u0925\u0947, \u091c\u093f\u0938\u092e\u0947\u0902 \u0935\u0947 \u092c\u0921\u093c\u0940 \u0914\u0930 \u091c\u091f\u093f\u0932 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u092a\u0940\u0938\u0915\u0930 \u091b\u094b\u091f\u0947-\u091b\u094b\u091f\u0947 \u0936\u0947\u0937\u092b\u0932 \u0928\u093f\u0915\u093e\u0932\u0924\u0947 \u0925\u0947, \u091c\u092c \u0924\u0915 \u0915\u093f \u0909\u0928\u094d\u0939\u0947\u0902 \u0938\u0939\u0940 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 \u0939\u0932 \u0928\u0939\u0940\u0902 \u092e\u093f\u0932 \u091c\u093e\u0924\u093e \u0925\u093e\u0964<\/span><\/span><span data-path-to-node=\"68,12\">. <\/span><span data-path-to-node=\"68,14\"><span class=\"citation-1608\">\u092f\u0939 \u092e\u0949\u0921\u094d\u092f\u0942\u0932\u0930 \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0915\u093e \u091c\u0928\u094d\u092e \u0925\u093e\u2014\u0935\u0939 &quot;\u0918\u0921\u093c\u0940 \u0917\u0923\u093f\u0924&quot; \u091c\u094b \u0939\u092e\u093e\u0930\u0940 \u0906\u0927\u0941\u0928\u093f\u0915 \u0926\u0941\u0928\u093f\u092f\u093e \u0915\u094b \u0938\u0941\u091a\u093e\u0930\u0942 \u0930\u0942\u092a \u0938\u0947 \u091a\u0932\u093e\u0924\u0940 \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"68,16\">. <\/span><span data-path-to-node=\"68,18\"><span class=\"citation-1607\">\u0906\u091c, \u091c\u092c \u092d\u0940 \u0906\u092a \u0938\u0941\u0930\u0915\u094d\u0937\u093f\u0924 \u0911\u0928\u0932\u093e\u0907\u0928 \u092c\u0948\u0902\u0915\u093f\u0902\u0917 \u092a\u093e\u0938\u0935\u0930\u094d\u0921 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0906\u092a \u0905\u092a\u0928\u0947 \u0921\u0947\u091f\u093e \u0915\u0940 \u0938\u0941\u0930\u0915\u094d\u0937\u093e \u0915\u0947 \u0932\u093f\u090f \u0906\u0930\u094d\u092f\u092d\u091f \u0915\u0947 \u0927\u093e\u0924\u0941 \u0915\u0947 \u092f\u0902\u0924\u094d\u0930 \u0915\u0947 \u0935\u0902\u0936\u091c \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930 \u0930\u0939\u0947 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964<\/span><\/span><span data-path-to-node=\"68,20\">.<\/span><\/p>\n<p data-path-to-node=\"69\"><b data-path-to-node=\"69\" data-index-in-node=\"0\">\u0938\u092e\u092f\u0930\u0947\u0916\u093e<\/b><\/p>\n<table data-path-to-node=\"70\">\n<thead>\n<tr>\n<td><strong>\u092e\u0940\u0932 \u0915\u093e \u092a\u0924\u094d\u0925\u0930<\/strong><\/td>\n<td><strong>\u0935\u093f\u0935\u0930\u0923<\/strong><\/td>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><span data-path-to-node=\"70,1,0,0\"><b data-path-to-node=\"70,1,0,0\" data-index-in-node=\"0\">\u092a\u0936\u094d\u091a\u093f\u092e\u0940 \u0938\u0902\u0926\u0930\u094d\u092d.<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_2c7e7ac57808f84c-419\" data-path-to-node=\"70,1,1,0\"><span data-path-to-node=\"70,1,1,0,1\"><span class=\"citation-1606\">1624 \u0908. (\u092c\u0948\u091a\u0947\u091f \u0921\u0947 \u092e\u0947\u091c\u093c\u093f\u0930\u093f\u092f\u093e\u0915) <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><span data-path-to-node=\"70,2,0,0\"><b data-path-to-node=\"70,2,0,0\" data-index-in-node=\"0\">\u092d\u093e\u0930\u0924\u0940\u092f \u0938\u094d\u0930\u094b\u0924<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_2c7e7ac57808f84c-420\" data-path-to-node=\"70,2,1,0\"><span data-path-to-node=\"70,2,1,0,1\"><span class=\"citation-1605\">499 \u0908\u0938\u094d\u0935\u0940 (\u0906\u0930\u094d\u092f\u092d\u091f) <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><span data-path-to-node=\"70,3,0,0\"><b data-path-to-node=\"70,3,0,0\" data-index-in-node=\"0\">\u0915\u093e\u0932 \u0905\u0902\u0924\u0930\u093e\u0932<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_2c7e7ac57808f84c-421\" data-path-to-node=\"70,3,1,0\"><span data-path-to-node=\"70,3,1,0,1\"><span class=\"citation-1604\">1,100 \u0935\u0930\u094d\u0937\u094b\u0902 \u0938\u0947 \u092d\u0940 \u0905\u0927\u093f\u0915 <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p data-path-to-node=\"71\"><b data-path-to-node=\"71\" data-index-in-node=\"0\">\u092e\u0942\u0932 \u092a\u093e\u0920<\/b><\/p>\n<blockquote data-path-to-node=\"72\">\n<p id=\"p-rc_2c7e7ac57808f84c-422\" data-path-to-node=\"72,0\"><span data-path-to-node=\"72,0,1\"><span class=\"citation-1603\">The <\/span><i data-path-to-node=\"72,0,1\" data-index-in-node=\"4\"><span class=\"citation-1603\">\u0906\u0930\u094d\u092f\u092d\u091f\u093f\u092f\u093e<\/span><\/i><span class=\"citation-1603\"> (\u0917\u0923\u093f\u0924\u093e 32-33) \u092e\u0947\u0902 \u0907\u0938 \u091a\u0942\u0930\u094d\u0923\u0940\u0915\u0930\u0923 \u0915\u094b \u0915\u094d\u0930\u093f\u092f\u093e\u0928\u094d\u0935\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092a\u094d\u0930\u092f\u0941\u0915\u094d\u0924 \u092a\u093e\u0930\u0938\u094d\u092a\u0930\u093f\u0915 \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u0940 \u091a\u0930\u0923-\u0926\u0930-\u091a\u0930\u0923 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u093e \u0935\u093f\u0938\u094d\u0924\u0943\u0924 \u0935\u0930\u094d\u0923\u0928 \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"72,0,3\">.<\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/blockquote>\n<p id=\"p-rc_2c7e7ac57808f84c-423\" data-path-to-node=\"73\"><span data-path-to-node=\"73,0\"><b data-path-to-node=\"73,0\" data-index-in-node=\"0\">\u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0928\u0935\u093e\u091a\u093e\u0930<\/b> <\/span><span data-path-to-node=\"73,2\"><span class=\"citation-1602\">The <\/span><i data-path-to-node=\"73,2\" data-index-in-node=\"4\"><span class=\"citation-1602\">\u0915\u0942\u091f\u091f\u0915<\/span><\/i><span class=\"citation-1602\"> \u092f\u0939 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u092e \u092a\u0939\u0932\u0940 \u092c\u093e\u0930 \u0925\u093e \u091c\u092c \u092e\u0949\u0921\u094d\u092f\u0942\u0932\u0930 \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0915\u093e \u092a\u094d\u0930\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0925\u093e\u0964<\/span><\/span><span data-path-to-node=\"73,4\">. <\/span><span data-path-to-node=\"73,6\"><span class=\"citation-1601\">\u0907\u0938 \u0935\u093f\u0927\u093f \u0915\u094b \u0905\u0915\u094d\u0938\u0930 \u0918\u0921\u093c\u0940 \u0914\u0930 \u0936\u0947\u0937\u092b\u0932 \u0917\u0923\u093f\u0924 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u091c\u093e\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"73,8\">. <\/span><span data-path-to-node=\"73,10\"><span class=\"citation-1600\">\u0917\u094d\u0930\u0939\u094b\u0902 \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u0914\u0930 \u0915\u0932\u093f\u092f\u0941\u0917 \u0915\u0947 \u092a\u094d\u0930\u093e\u0930\u0902\u092d \u0938\u0947 \u0905\u092c \u0924\u0915 \u0915\u093f\u0924\u0928\u0947 \u0926\u093f\u0928 \u092c\u0940\u0924 \u091a\u0941\u0915\u0947 \u0939\u0948\u0902, \u092f\u0939 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0907\u0938 \u0935\u093f\u0927\u093f \u0915\u093e \u0935\u093f\u0915\u093e\u0938 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0925\u093e\u0964<\/span><\/span><span data-path-to-node=\"73,12\">.<\/span><\/p>\n<p id=\"p-rc_2c7e7ac57808f84c-424\" data-path-to-node=\"74\"><span data-path-to-node=\"74,0\"><b data-path-to-node=\"74,0\" data-index-in-node=\"0\">\u092e\u091c\u0947\u0926\u093e\u0930 \u0924\u0925\u094d\u092f<\/b> <\/span><span data-path-to-node=\"74,2\"><span class=\"citation-1599\">\u0907\u0938 \u0935\u093f\u0927\u093f \u0915\u094b &#039;\u092a\u0932\u094d\u0935\u0930\u093e\u0907\u091c\u093c\u0930&#039; \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u092f\u0939 \u0917\u0941\u0923\u093e\u0902\u0915\u094b\u0902 \u0915\u094b \u091b\u094b\u091f\u0947 \u0938\u0947 \u091b\u094b\u091f\u0947 \u091f\u0941\u0915\u0921\u093c\u094b\u0902 \u092e\u0947\u0902 \u0924\u094b\u0921\u093c \u0926\u0947\u0924\u0940 \u0939\u0948, \u0920\u0940\u0915 \u0909\u0938\u0940 \u0924\u0930\u0939 \u091c\u0948\u0938\u0947 \u0905\u0928\u093e\u091c \u0915\u094b \u092a\u0940\u0938\u0915\u0930 \u0906\u091f\u093e \u092c\u0928\u093e\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"74,4\">.<\/span><\/p>\n<p id=\"p-rc_2c7e7ac57808f84c-425\" data-path-to-node=\"75\"><span data-path-to-node=\"75,0\"><b data-path-to-node=\"75,0\" data-index-in-node=\"0\">\u0906\u0927\u0941\u0928\u093f\u0915 \u0935\u093f\u0930\u093e\u0938\u0924<\/b> <\/span><span data-path-to-node=\"75,2\"><span class=\"citation-1598\">\u092f\u0939 \u0926\u0943\u0937\u094d\u091f\u093f\u0915\u094b\u0923 \u0911\u0928\u0932\u093e\u0907\u0928 \u092c\u0948\u0902\u0915\u093f\u0902\u0917 \u0915\u0940 \u0938\u0941\u0930\u0915\u094d\u0937\u093e \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u090f \u091c\u093e\u0928\u0947 \u0935\u093e\u0932\u0947 \u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u090f\u0928\u094d\u0915\u094d\u0930\u093f\u092a\u094d\u0936\u0928 (\u0906\u0930\u090f\u0938\u090f \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u092e) \u0915\u093e \u0906\u0927\u093e\u0930 \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"75,4\">.<\/span><\/p>\n<\/div><\/div><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":3513,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[74],"tags":[544,556,559,615,612,614,613],"class_list":["post-3646","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics","tag-ancient-indian-mathematics","tag-aryabhata","tag-aryabhatiya","tag-cryptography-roots","tag-kuttaka","tag-modular-arithmetic","tag-pulveriser"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\r\n<title>The Pulveriser (Kuttaka) \u2013 Grinding Down the Numbers - BharatWisdom<\/title>\r\n<meta name=\"description\" content=\"Excerpt\" \/>\r\n<meta name=\"robots\" content=\"index, follow, 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