Question

The GCD of 364 and 462 is

• A. $3$
• B. $11$
• C. $14$
• D. $7$

Hint:

GCD can be found by Euclidean algorithm.

Answer 1

The Correct Option is C

To solve the problem of finding the Greatest Common Divisor (GCD) of 364 and 462, we'll use the Euclidean algorithm. The GCD is the largest positive integer that divides both numbers without leaving a remainder.

1. Apply the Euclidean algorithm:
   1. Divide 462 by 364 and find the remainder:
      • \(462 \div 364 = 1\) remainder \(462 - 364 \times 1 = 98\).
   2. Now, divide 364 by the remainder 98:
      • \(364 \div 98 = 3\) remainder \(364 - 98 \times 3 = 70\).
   3. Next, divide 98 by 70:
      • \(98 \div 70 = 1\) remainder \(98 - 70 \times 1 = 28\).
   4. Continue with 70 and 28:
      • \(70 \div 28 = 2\) remainder \(70 - 28 \times 2 = 14\).
   5. Finally, divide 28 by 14:
      • \(28 \div 14 = 2\) remainder \(28 - 14 \times 2 = 0\).
2. When the remainder reaches 0, the divisor at that step is the GCD. Here, the GCD is 14.

Therefore, the GCD of 364 and 462 is 14.