Multiple choice

Find the largest positive integer that will divide $122, 150, $ and $115$ leaving remainder $5, 7$ and $11$ respectively.

  1. $3$
  2. $2$
  3. $13$
  4. $11$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The number must divide (122-5)=117, (150-7)=143, and (115-11)=104. GCD(117, 143, 104) = GCD(9*13, 11*13, 8*13) = 13.

AI explanation

Subtract the respective remainders from the numbers to get 117, 143, and 104. The required largest number is the HCF of 117, 143, and 104. Factoring them gives 117 = 13 times 9, 143 = 13 times 11, and 104 = 13 times 8. Since 9, 11, and 8 share no common factors, the HCF is 13.

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