50{×}29(mod15)

Answer 1

To calculate \( 50 \times 29 \mod 15 \), we can first simplify \( 50 \mod 15 \) and \( 29 \mod 15 \).

1. Calculate \( 50 \mod 15 \): \[ 50 \div 15 = 3 \quad (\text{which gives a quotient of 3 and a remainder of } 5) \] Therefore, \( 50 \mod 15 = 5 \).

2. Calculate \( 29 \mod 15 \): \[ 29 \div 15 = 1 \quad (\text{which gives a quotient of 1 and a remainder of } 14) \] Therefore, \( 29 \mod 15 = 14 \).

Now we can multiply the results: \[ 50 \times 29 \mod 15 = (50 \mod 15) \times (29 \mod 15) \mod 15 = 5 \times 14 \mod 15 \]

Now calculate \( 5 \times 14 = 70 \).

Finally, we find \( 70 \mod 15 \): \[ 70 \div 15 = 4 \quad (\text{which gives a quotient of 4 and a remainder of } 10) \] Thus, \( 70 \mod 15 = 10 \).

The final result is: \[ \boxed{10} \]