find the largest number which divides 245 and 1029 leaving remainder 5 in each case.

Required number = HCF of (245-5) and (1029-5) = HCF of 240 and 1024

Now, HCF of 240 and 1024 can be find out by prime factorisation method as:

240 = 2 × 2 × 2 × 2 × 3 × 5 and

1024 = 2 × 2 × 2 × 2 × 2 × 2 ×2 × 2 × 2 × 2

Therefore HCF of 240 and 1024 = 2 × 2 × 2 × 2 = 16

Hence, 16 is the largest number which divides 245 and 1029 and leaves the remainder 5 in each case.

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