To solve this problem, we can use the concept of remainders and modular arithmetic.

Let's denote the number as x. We are given that when x is divided by 779, the remainder is 47. Mathematically, we can write this as:

x ≡ 47 (mod 779)

This means that x is congruent to 47 modulo 779. In other words, x leaves a remainder of 47 when divided by 779.

To find the remainder when x is divided by 19, we can use the concept of modular arithmetic. We can rewrite the congruence relation as:

x ≡ 47 + 779k (mod 779)

Here, k is an integer representing the number of times x is divisible by 779. Since 779 is divisible by 19 (779 = 19 * 41), we can further simplify the congruence relation as:

x ≡ 47 + 19 * 41k (mod 779)

Now, let's consider the possible values of k. Since k is an integer, it can take any value from -∞ to +∞. However, we are only interested in finding the remainder when x is divided by 19. The remainder can be any integer from 0 to 18.

Let's consider the values of k that would give us the remainder of 0 when x is divided by 19. We need to find the smallest positive integer value of k that satisfies the congruence relation:

47 + 19 * 41k ≡ 0 (mod 19)

Simplifying this equation, we get:

47 + 19 * 41k ≡ 0 (mod 19)
47 ≡ 0 (mod 19)

Since 47 is not congruent to 0 modulo 19, we need to increase the value of k until we find a value that satisfies the congruence relation. The first value of k that satisfies the congruence relation is k = 1:

47 + 19 * 41 * 1 ≡ 0 (mod 19)

This means that when x is divided by 19, the remainder is 0.

Therefore, the correct answer is option (a) 0.

When the number is divided by 779, let the quotient obtained be k.