Question

find the largest number which divides 245 and 1029 leaving remainder 5 in each case.
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Answer 1

≡QUESTION≡

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

                                                       

║⊕ANSWER⊕║

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

                               = HCF of 240 and 1024

(∵ 5 is the remainder)

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

240 = 2 × 2 × 2 × 2 × 3 × 5

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

∴ 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.