A number when divided by 729 gives a remainder of 56. What will we get as remainder if the same number is divided by 27 ?

Options

A. 4
B. 2
C. 0
D. 1

Answer

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

### Step 1: Define the number
Let the number be \( N \).

### Step 2: Express the number in terms of the divisor and remainder
According to the problem, when \( N \) is divided by 729, it gives a remainder of 56. This can be expressed mathematically as:
\[ N = 729k + 56 \]
where \( k \) is some integer.

### Step 3: Rewrite the expression in terms of the new divisor
Now, we need to find the remainder when \( N \) is divided by 27. We can rewrite \( N \) as follows:
\[ N = 729k + 56 = (27 \cdot 27)k + 56 \]
This shows that \( 729 \) can be expressed as \( 27 \cdot 27 \).

### Step 4: Simplify the expression
Now, we can express \( N \) in terms of 27:
\[ N = 27(27k) + 56 \]

### Step 5: Find the remainder of 56 when divided by 27
Next, we need to find the remainder when 56 is divided by 27. We can perform the division:
\[ 56 \div 27 = 2 \quad \text{(since } 27 \times 2 = 54\text{)} \]
The remainder can be calculated as:
\[ 56 - 54 = 2 \]

### Step 6: Conclusion
Thus, when \( N \) is divided by 27, the remainder is:
\[ \text{Remainder} = 2 \]

### Final Answer
The remainder when the number is divided by 27 is **2**.

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