What is the largest number that will divide both 60 and 100 perfectly, with no remainder?

• A. 10
• B. 20
• C. 25
• D. 30

Answer: (B)

Greatest common divisor is the idea here. To find it, prime-factorize both numbers: 60 = 2^2 × 3 × 5 and 100 = 2^2 × 5^2. The common prime factors are 2 and 5. Taking the smallest powers that appear in both numbers gives 2^2 and 5^1, so multiply: 2^2 × 5 = 4 × 5 = 20. That means 20 divides both 60 and 100 evenly (60 ÷ 20 = 3 and 100 ÷ 20 = 5). Any larger number wouldn’t divide both because it would require higher powers that aren’t present in both. For comparison, 25 doesn’t divide 60, and 30 doesn’t divide 100, while 10 is smaller than 20.