Multiple choice

Find the greatest number from the options that will divide $1025, 1299$ and $1575$ leaving remainders $5,7$ and $11$ respectively.

  1. $70$
  2. $78$
  3. $68$
  4. $98$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The number must divide (1025-5)=1020, (1299-7)=1292, and (1575-11)=1564. The greatest such number is the HCF of 1020, 1292, and 1564. HCF(1020, 1292) = 68, and 1564 is divisible by 68.

AI explanation

Subtract the remainders from the respective numbers to find the target multiples: 1020, 1292 and 1564. Testing the highest common factor of these differences, we see that 68 divides 1020 exactly 15 times, 1292 exactly 19 times, and 1564 exactly 23 times. Therefore, 68 is the required number.

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