Question

What is the remainder when 34,901 is divided by 26? (1 point) Responses 0 0 6 6 9 9 12

Answer 1

To find the remainder when 34,901 is divided by 26, we can perform a division and find the remainder directly.

First, we divide 34,901 by 26:
- Dividing 34,901 by 26 gives approximately 1346.230769.
- To find the whole number part, we consider 1346.

Next, we multiply 1346 by 26:
\[ 1346 \times 26 = 34,996 \]

Now, to find the remainder, we need to subtract:
\[ 34,901 - 34,996 = -95 \]

Since we've gone negative, we can adjust by finding how far we need to go back:
\[ -95 + 26 = -69 \]
\[ -69 + 26 = -43 \]
\[ -43 + 26 = -17 \]
\[ -17 + 26 = 9 \]

This positive value of 9 becomes our remainder.

Alternatively, to simplify our calculations, we can compute directly:
1. \( 34,901 \div 26 \approx 1346 \)
2. \( 1346 \times 26 = 34,996 \)
3. \( 34,901 - 34,996 = -95 \)

By the above steps, the benchmark method confirms that the remainder can be quickly computed by downward adjustments:
The final modulo operation confirms the remainder when taking \( 34,901 \):

Hence, the remainder when 34,901 is divided by 26 is **9**.