Question

the greatest number which divides 245 and 1029 use a remainder 5 in each case

Answer 1

Hi friend.
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Your answer would be,

To calculate that no we need to find the HCF of those two nos which gives 5 as remainder,
Therefore, the required number = HCF of (245-5) and (1029-5) that is HCF of 240 and 1024.

Now,
HCF of 240 and 1024 can be calculated by prime factorisation method :

=>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
Therefore the largest no which when divided by 245 and 1029 leaves a remainder of 5 is 16 (ans)
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Hope it helps you friend.
Thank you.