Q. 333.5( 2 Votes )

Find the largest number dividing 230 and 142 and leaving remainders 5 and 7 respectively.

Answer :

Let k be the largest number dividing 230 and 142 leaving remainders 5 and 7 respectively.

Therefore, we can write 230 = ka + 5 and 142 = kb + 7


Where, a, b


230 = ka + 5 142 = kb + 7


ka = 230 – 5 kb = 142 – 7


ka = 225 kb = 135


But, k is the largest number.


So, k becomes the largest divisor, g. c. d of 225 and 135


225 = 5 × 5 × 3 × 3


135 = 5 × 3 × 3 × 3


Therefore, g. c. d(225, 135) = k


g. c. d(225, 135) = 5 × 3 × 3 = 45


k = 45


Therefore, the largest number dividing 230 and 142 leaving remainders 5 and 7 respectively is 45.


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