Multiple choice

A natural number N, when divides 50, 75 and 125 leaves remainders 2, 3 and 5 respectively. Find the maximum value of N?

  1. 8

  2. 12

  3. 16

  4. 24
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D Correct answer
Explanation

N must divide (50-2)=48, (75-3)=72, and (125-5)=120. The maximum value of N is the greatest common divisor (GCD) of 48, 72, and 120. The GCD(48, 72, 120) = 24.

AI explanation

The natural number N leaves the same difference between each dividend and its remainder, as 50 minus 2 is 48, 75 minus 3 is 72, and 125 minus 5 is 120. Therefore, N must be a factor of the highest common factor (HCF) of 48, 72 and 120. The HCF is 24, making 24 the maximum possible value for N.

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