Multiple choice

Find the greatest number that will divide $152, 245$ and $616$ leaving remainders $8, 5$ and $4$ respectively.

  1. $6$
  2. $8$
  3. $12$
  4. $16$
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C Correct answer
Explanation

Subtract the remainders: 152-8=144, 245-5=240, 616-4=612. The greatest number is the HCF of 144, 240, and 612. HCF(144, 240) = 48. HCF(48, 612) = 12.

AI explanation

To find the greatest number, we subtract the respective remainders from the given numbers to get 144, 240 and 612. The required number is the highest common factor of these three differences. Using prime factorization, the highest common factor of 144, 240 and 612 is 12.

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