Question

If the Euclidean algorithm equation is given as \( a = bq + r \) where \( b = 43 \), \( q = 31 \), and \( r = 32 \), then the value of \( a \) is:

• A. \( 1365 \)
• B. \( 1356 \)
• C. \( 1360 \)
• D. \( 1350 \)

Hint:

The Euclidean division algorithm states: \[ a = bq + r, \] where \( a \) is the dividend, \( b \) is the divisor, \( q \) is the quotient, and \( r \) is the remainder.

Answer 1

The Correct Option is A

The Euclidean division algorithm states that: \[ a = bq + r. \] Substituting the given values: \[ a = 43 \times 31 + \] \[ a = 1333 + \] \[ a = 13 \]