Question

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

• A. $3$
• B. $2$
• C. $13$
• D. $11$

Answer 1

Answer: (C)

$13$

As the largest positive integer that will divide 122, 150 and 115 leaves remainder 5, 7 and 11 respectively.

Therefore,

$122-5=117$

$150-7=143$

$115-11=104$

$\because$ The HCF of 104, 117 and 143 is 13

Hence, the largest number which divides 122, 150 and 115 leaving 5, 7 and 11 as remainders respectively is 13.