When a number is divided by 52, remainder is obtained 45. If the same number is divided by 13, the remainder ?

Options

A. 5
B. 6
C. 12
D. 7

Answer

To solve the problem step by step, we can follow these instructions:

1. **Understand the Problem**: We have a number \( n \) that when divided by 52 gives a remainder of 45. We need to find the remainder when the same number \( n \) is divided by 13.

2. **Express the Number**: Since \( n \) gives a remainder of 45 when divided by 52, we can express \( n \) in the form:
\[ n = 52k + 45 \]
where \( k \) is some integer.

3. **Find the Remainder with 13**: Now, we need to find \( n \mod 13 \). We can substitute \( n \) into the equation:
\[ n \mod 13 = (52k + 45) \mod 13 \]

4. **Simplify \( 52k \mod 13 \)**: We know that \( 52 \) is a multiple of \( 13 \):
\[ 52 \mod 13 = 0 \]
Therefore, \( 52k \mod 13 = 0 \).

5. **Calculate \( 45 \mod 13 \)**: Now we need to find \( 45 \mod 13 \):
\[ 45 \div 13 = 3 \quad \text{(which gives us a quotient of 3)} \]
\[ 3 \times 13 = 39 \]
\[ 45 - 39 = 6 \]
Thus, \( 45 \mod 13 = 6 \).

6. **Combine the Results**: Since \( 52k \mod 13 = 0 \) and \( 45 \mod 13 = 6 \), we have:
\[ n \mod 13 = 0 + 6 = 6 \]

7. **Conclusion**: Therefore, the remainder when the number \( n \) is divided by 13 is:
\[ \boxed{6} \]