Multiple choice

The greatest number which divides $261, 933\ and \ 1381$ leaving remainders $5$ in each case is

  1. $128$
  2. $64$
  3. $32$
  4. $16$
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C Correct answer
Explanation

Subtract the remainder 5 from each number: 256, 928, 1376. The HCF of these numbers is 32.

AI explanation

Subtract the common remainder of 5 from each number to get 256, 928, and 1376. Using the Euclidean algorithm to find the highest common factor, the HCF of 256 and 928 is 32, and 32 also perfectly divides 1376. Therefore, the required greatest number is 32.

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