Question

Find the greatest no. Which divides 34,60, and 85 leaving remainder of 7,6 and 4 respectivly

Answer 1

$\huge\mathbb{SOLUTION:-}$

• We have to find the greatest number which divides 34,60and 85 an leave remainder 7,6,4

$\bf\underline{\red{\:\: According\:To\: Question}}$

$\sf \bullet 34-7= 27\\ \\ \sf \bullet 60-6= 54\\ \\ \sf \bullet 85-4= 81$

Now their H.C.F by Euclid division lemma

$\sf \leadsto{\blue{ H.C.F \:of\:27\: and\:54}}\\ \\ \sf\leadsto 54= 27\times 2+0\\ \\ \sf\implies H.C.F \:of\:27\:and\:54= 27$

• Now H.C.F of 27 and 81

$\sf \leadsto {\purple{H.C.F \:of\:27\: and\:81}}\\ \\ \sf\leadsto 81= 27\times 3+0\\ \\ \sf\implies H.C.F \:of\:27\:and\:81= 27$

• Their H.C.F is 27

• So the greatest number that's divides is 27

$\boxed{\sf{\red{The\:number\:is\:27}}}$