What is the greatest common divisor of 28 and 35?

• A. 7
• B. 14
• C. 28
• D. 35

Answer: (A)

Finding the greatest common divisor means identifying the largest number that divides both numbers evenly. For 28 and 35, factor each: 28 = 2^2 × 7, 35 = 5 × 7. The only common factor is 7, so the largest one they share is 7. You can also confirm with the Euclidean method: gcd(28,35) = gcd(28,35 − 28) = gcd(28,7) = gcd(7,0) = 7. The other options don’t work because 14 divides 28 but not 35, while 28 and 35 don’t divide the other number. So the greatest common divisor is 7.