The largest number that will divide 789, 861, and 1069 leaving the remainders 7, 11, and 15 respectively is:

Correct option is C

Given:

When dividing:
789 → remainder 7
861 → remainder 11
1069 → remainder 15

Concept used:
If a number leaves different remainders, subtract those remainders from each number first.
Then find the HCF (highest common factor) of the resulting numbers.

Solution:
789 − 7 = 782
861 − 11 = 850
1069 − 15 = 1054

Now find HCF of 782, 850, 1054

850 − 782 = 68
1054 − 850 = 204

HCF(782, 850, 1054) = HCF(68, 204)

204 ÷ 68 = 3 exactly → remainder 0

So, HCF = 68

Now check given options: 68 not listed, but 68 = 34 × 2
→ 34 divides all numbers too.

Thus, largest number = 34

Correct answer is (c) 34.