1. Using the Euclidian algorithm, compute (91,39) and (73,21)

Answer:HCF(91,39) = 13 and HCF(73,21) = 1Step-by-step explanation:As per euclidian algorithm, a = bq + r, where a is dividend, b is divisor, q is quotient and r is remainder.We can use euclidian algorithm to find the HCF of numbers.To find: HCF ( 91, 39 ):On dividing 91 by 39, we get91=39×2+13Here, remainder = 13 [tex]\neq 0[/tex]So, again applying division algorithm on 39 and 13, we get[tex]39=13\times 3+0[/tex]As remainder = 0 and divisor at this step is equal to 13, HCF = 13 .To find: HCF ( 73, 21 )On dividing 73 by 21, we get[tex]73=21\times 3+10[/tex]Here, remainder = 10 [tex]\neq 0[/tex]On applying division algorithm on 21 and 10, we get[tex]21=10\times 2+1[/tex]Here, remainder = 1 [tex]\neq 0[/tex]On applying division algorithm on 10 and 1, we get[tex]10=1\times 10+0[/tex]As remainder = 0 and divisor at this step is 1, HCF = 1