Let the number be denoted by $N$. According to the problem, when $N$ is divided by 893, the remainder is 193. This can be written as:

$N = 893k + 193$ for some integer $k$.

Now, we need to find the remainder when $N$ is divided by 47. Substituting $N = 893k + 193$ into this, we get:

$N \mod 47 = (893k + 193) \mod 47$

Using the property of mod, we can split this expression as:

$N \mod 47 = (893k \mod 47 + 193 \mod 47)$

Step 1: Calculate $893 \mod 47$

We can now divide 893 by 47 to get the remainder:

$893 \div 47 = 19 \text{ with a remainder of } 0$

Thus,

$893 \mod 47 = 0$

Step 2: Calculate $193 \mod 47$

Now, divide 193 by 47:

$193 \div 47 = 4 \text{ with a remainder of } 5$

Thus,

$193 \mod 47 = 5$

Final Calculation

Now we substitute back:

$N \mod 47 = (0 + 5) = 5$

So, the remainder when $N$ is divided by 47 is $\boxed{5}$.

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Would you like further clarification on this? Here are some related questions:

1. How is the modulus operation applied in division?
2. Can we use the same approach for larger divisors?
3. What happens if the remainder in a division is negative?
4. How would this change if the remainder when dividing by 893 was different?
5. How can you calculate the remainder when dividing large numbers quickly?

Tip: The modulus operation is often used in number theory to manage remainders and cycles, especially when working with congruences.