Question

Find the largest positive integer that will be divide 122, 150 ,115 leaving remainders 5 7 11 respectively

Answer 1

this is your answer.☝

Answer 2

Answer:

The largest positive integer is 13.

Solution:

Let that largest positive integer be x.  

Given, when 122 is divided by x, it leaves the remainder 5

Thus, (122-5) is divisible by x, i.e. 117 is divisible by x.  

Given, when 150 is divided by x, it leaves remainder 7

Thus, (150-7) is divisible by x, i.e. 143 is divisible by x.  

Given, when 115 is divided by x, it leaves remainder 11

Thus, (115-11) is divisible by x, i.e. 104 is divisible by x.  

Hence, x = H. C. F. of 117, 143, 104.

Factors of 117 = 3 × 3 × 13

Factors of 143 = 11 × 13

Factors of 104 = 2 × 2 × 2 × 13

Thus, H. C. F. of 117, 143, 104 = 13

Then, 13 is the largest number which will divide 117, 143, 104 and leaving the remainders as 5, 7, 11.