Q. 345.0( 1 Vote )

Find the largest number dividing 110, 62, 92 and leaving remainders 5, 6 and 1 respectively.

Answer :

Let k be the largest number dividing 110, 62 and 92 leaving remainders 5, 6 and 1 respectively.

Therefore, we can write 110 = ka + 5, 62 = kb + 6 and 92 = kc + 1


Where, a, b and c


110 = ka + 5 62 = kb + 6 92 = kc + 1


ka = 110 – 5 kb = 62 – 6 kc = 92 – 1


ka = 105 kb = 56 kc = 91


But, k is the largest number.


So, k becomes the largest divisor, g. c. d of 105, 56 and 91


105 = 5 × 3 × 7


56 = 7 × 2 × 2 × 2


91 = 7 × 13


Therefore, g. c. d(105, 56, 91) = k


g. c. d(105, 56, 91) = 7


k = 7


Therefore, the largest number dividing 110, 62 and 92 leaving remainders 5, 6 and 1 respectively is 7.


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