Question
Work the modular arithmetic problem. \[ \begin{array}{l}(13 \cdot 5)(\bmod 4) \\ (13 \cdot 5)(\bmod 4)=\square(\bmod 4)\end{array} \]
Ask by Stanley Burgess. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\[
(13 \cdot 5)(\bmod 4) = 1(\bmod 4)
\]
Solution
We start by computing the product:
\[
13 \cdot 5 = 65
\]
Next, we find the remainder when \(65\) is divided by \(4\). Since
\[
4 \times 16 = 64,
\]
the remainder is:
\[
65 - 64 = 1.
\]
Thus, we have:
\[
(13 \cdot 5)(\bmod 4) = 1(\bmod 4).
\]
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Simplify this solution Mind Expander
To solve the problem, we first need to compute \(13 \cdot 5\): \[ 13 \cdot 5 = 65 \] Now we need to find \(65 \mod 4\). To do this, we divide 65 by 4, which gives us: \[ 65 \div 4 = 16 \quad \text{(with a remainder)} \] Calculating the exact remainder: \[ 16 \cdot 4 = 64 \] \[ 65 - 64 = 1 \] Thus, \[ 65 \mod 4 = 1 \] So, \[ (13 \cdot 5)(\bmod 4) = 1(\bmod 4) \] The final answer is: \[ \boxed{1} \]
