Which of the following is the greatest number which divides 1658 and 2041 leaving remainders 7 and 9, respectively?

Correct option is A

Given:

The numbers are 1658 and 2041.

Remainders are 7 and 9 respectively when divided by the required number.

Solution:

Subtract the remainders from the given numbers:

1658 - 7 = 1651

2041 - 9 = 2032

Now, find the HCF of 1651 and 2032 using the Euclidean algorithm:

2$$032 \div 1651 = 1 \, (\text{remainder} = 381)$$​

​$$1651 \div 381 = 4 \, (\text{remainder} = 127)$$​

38$$1 \div 127 = 3 \, (\text{remainder} = 0)$$​

When the remainder becomes 0, the divisor is the HCF.

Therefore, HCF = 127.

Thus, the greatest number that divides 1658 and 2041 leaving remainders 7 and 9 respectively is 127.