Multiple choice

Find the largest number that divides $2053$ and $967$ and leaves a remainder of $5$ and $7$ respectively.

  1. $64$
  2. $35$
  3. $96$
  4. $72$
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A Correct answer
Explanation

We need the largest number that divides 2053 leaving remainder 5 and 967 leaving remainder 7. This is the HCF of (2053 - 5) and (967 - 7), which is the HCF of 2048 and 960. The HCF of 2048 and 960 is 64.

AI explanation

Subtract the respective remainders from the numbers to get the exact multiples, yielding 2048 and 960. The largest number that divides both is their highest common factor. Using prime factorization or successive division, the highest common factor of 2048 and 960 is 64.

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