When a number is divided by 893 the remainder is 193. If the same number 

is divided by 47, the remainder will be :

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 \( \boxed{5} \).

---

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.

When a number is divided by 893 the remainder is 193. If the same number is divided by 47, the remainder will be:

Learn how to find the remainder when a number is divided by 47, given that the remainder when divided by 893 is 193. This solution uses modular arithmetic and division algorithms, making it suitable for students in Grades 9-11.

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