A number when divided by 14 leaves a remainder of 8, but when the same number is divided by 7, it well leave the remainder :

Options

A. 3
B. 5
C. 1
D. 7

Answer

To solve the problem step by step, let's denote the number as \( n \).

### Step 1: Understand the condition given
We know that when the number \( n \) is divided by 14, it leaves a remainder of 8. This can be expressed mathematically as:
\[ n = 14k + 8 \]
where \( k \) is some integer.

### Step 2: Rewrite the expression for \( n \)
From the equation above, we can see that \( n \) can take on values like:
- If \( k = 0 \), then \( n = 8 \)
- If \( k = 1 \), then \( n = 22 \)
- If \( k = 2 \), then \( n = 36 \)
- If \( k = 3 \), then \( n = 50 \)
- And so on...

### Step 3: Find the remainder when \( n \) is divided by 7
Now, we need to find the remainder when \( n \) is divided by 7. We can substitute our expression for \( n \) into the division by 7:
\[ n = 14k + 8 \]

When we divide \( n \) by 7, we can simplify:
\[ n \mod 7 = (14k + 8) \mod 7 \]

### Step 4: Simplify the expression
Since \( 14 \mod 7 = 0 \), we have:
\[ n \mod 7 = (0 + 8) \mod 7 \]
\[ n \mod 7 = 8 \mod 7 \]

### Step 5: Calculate \( 8 \mod 7 \)
Now, we calculate the remainder:
\[ 8 \div 7 = 1 \quad \text{(which gives a quotient of 1 and a remainder of 1)} \]
Thus,
\[ 8 \mod 7 = 1 \]

### Conclusion
Therefore, when the number \( n \) is divided by 7, it leaves a remainder of 1.

### Final Answer
The remainder when the number is divided by 7 is **1**.

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