Question

find the greatest number which can divide 89 53 and 77 and leave a remainder of 5 in each case​

Answer 1

The Greatest Number required is the HCF of 89, 53 and 77

Using Euclid's Division Lemma

a = bq+r

HCF(89,53)

-» 89 = 53 * 1 + 36

-» 53 = 36 * 1 + 17

-» 36 = 17 * 2 + 2

-» 17 = 2 * 8 + 1

-» 2 = 1 * 2 + 0

Therefore, HCF (89,53) = 1

Now, HCF( 89,53,77) = HCF( 1,77)

77 = 1 * 77 + 0

Therefore, HCF(89,53,77) = 1

Therefore, the highest number which divides the numbers 89,53,77 is 1