Multiple choice

The greatest number which divides $77, \,147$ and $252$ leaving the same remainder $7$ in each case is

  1. $9$
  2. $15$
  3. $25$
  4. $35$
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D Correct answer
Explanation

The greatest number that divides 77, 147, and 252 leaving a remainder of 7 is the HCF of (77-7), (147-7), and (252-7). This is the HCF of 70, 140, and 245. The HCF is 35.

AI explanation

To find the greatest number that leaves the same remainder, we use the property that the number must perfectly divide the differences between the given values. The differences between the numbers are 147 minus 77 equals 70, 252 minus 147 equals 105, and 252 minus 77 equals 175. The highest common factor of 70, 105 and 175 is 35.

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