When a number is divided by 63 the remainder is obtained as 26. What will be the remainder when the number is divided by 3?

Options

A. 1
B. 2
C. 3
D. 5

Answer

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

### Step 1: Understand the given information
According to the problem, when the number \( x \) is divided by 63, the remainder is 26. This can be expressed mathematically as:
\[ x = 63k + 26 \]
where \( k \) is some integer (the quotient).

### Step 2: Find the relationship with 3
We need to find the remainder when \( x \) is divided by 3. We can rewrite the equation for \( x \):
\[ x = 63k + 26 \]

### Step 3: Calculate \( 63 \mod 3 \)
Now, we will find \( 63 \mod 3 \):
\[ 63 \div 3 = 21 \quad \text{(exactly, so the remainder is 0)} \]
Thus,
\[ 63 \equiv 0 \mod 3 \]

### Step 4: Calculate \( 26 \mod 3 \)
Next, we need to find \( 26 \mod 3 \):
\[ 26 \div 3 = 8 \quad \text{(with a remainder of 2)} \]
So,
\[ 26 \equiv 2 \mod 3 \]

### Step 5: Combine the results
Now, substituting back into our equation for \( x \):
\[ x \equiv 63k + 26 \mod 3 \]
Since \( 63k \equiv 0 \mod 3 \), we have:
\[ x \equiv 0 + 2 \mod 3 \]
Thus,
\[ x \equiv 2 \mod 3 \]

### Conclusion
The remainder when the number \( x \) is divided by 3 is **2**.