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Question

Find the largest number by which when 245and 1029 are divided, remainder in each case is 5.


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Solution

The largest number which divides 245 and 1029, gets remainder 5.

The number which is exactly divisible is 245-5=240 and 1029-5=1024

Prime factorization of 240 and 1024 are

240=2×2×2×2×3×51024=2×2×2×2×2×2×2×2×2×2

Common factors are 2,2,2,2

H.C.F of 240 and 1024 is 2×2×2×2=16

Hence, the largest number by which when 245and 1029 are divided and gives remainder 5 is 16.


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