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| 1. |
Find the HCF of 612 and 1314 using prime factorisation. |
| Answer» We have, 612 and 1314{tex} \\therefore \\quad 612 = ( 2 \\times 2 \\times 3 \\times 3 \\times 17 ) = \\left( 2 ^ { 2 } \\times 3 ^ { 2 } \\times 17 \\right){/tex}and {tex}1314 = ( 2 \\times 3 \\times 3 \\times 73 ) = \\left( 2 \\times 3 ^ { 2 } \\times 73 \\right){/tex}.{tex}\\therefore{/tex}\xa0HCF (612,1314) = product of common terms with lowest power{tex}= \\left( 2 \\times 3 ^ { 2 } \\right) = ( 2 \\times 9 ) {/tex}HCF (612,1314) = 18and LCM (612, 1314) = product of prime factors with highest power{tex}= \\left( 2 ^ { 2 } \\times 3 ^ { 2 } \\times 17 \\times 73 \\right) = ( 4 \\times 9 \\times 17 \\times 73 ){/tex}LCM (612, 1314) = 44676.Hence, HCF(612, 1314) = 18and LCM(612, 1314) = 44676. | |