Question

Find the greatest number that can divide 245 and 1029, so as to leave remainder 5 in
each case.

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Answer 1

Answer:

It is given that required number which divides 245 and 1029, the remainder is 5 in each case. ⇒ 245 - 5 = 240 and 1029 - 5 = 1024 are completely divisible by the required number. Since, it is given that the required number is the largest number. Therefore, it is the HCF of 240 and 1024.

Answer 2

To Find:

• The greatest number that can divide the 245 and 1029 and leave remainder 5 in each case.

Subtracting 5 from both the number:

• 245 - 5 = 240
• 1029 - 5 = 1024

Finding the greatest number:

Using prime factorisation method.

• Factors of 240 = 2⁴ × 3 × 5
• Factors of 1024 = 2¹⁰

HCF (240, 1024) = 2⁴ = 16

Hence,

• The greatest number is 16.