Use the definition of GCD, not a calculation, to complete parts (a) through (c). (a) \( \operatorname{GCD}(60,60) \) (b) \( \operatorname{GCD}(16,160) \) (c) \( \operatorname{GCD}(66,0) \) (a) \( \operatorname{GCD}(60,60)=\square \)

To find the GCD (Greatest Common Divisor) of two numbers, we use the definition that the GCD of two integers \( a \) and \( b \) is the largest positive integer \( d \) that divides both \( a \) and \( b \) without leaving a remainder. Let's solve each part step by step: ### (a) \( \operatorname{GCD}(60, 60) \) 1. **Identify the numbers**: Here, both numbers are 60. 2. **Divisors of 60**: The positive divisors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. 3. **Common divisors**: Since both numbers are the same, all divisors of 60 are common to both. 4. **Largest common divisor**: The largest divisor is 60 itself. Thus, \( \operatorname{GCD}(60, 60) = 60 \). ### (b) \( \operatorname{GCD}(16, 160) \) 1. **Identify the numbers**: The numbers are 16 and 160. 2. **Divisors of 16**: The positive divisors of 16 are 1, 2, 4, 8, and 16. 3. **Divisors of 160**: The positive divisors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, and 160. 4. **Common divisors**: The common divisors of 16 and 160 are 1, 2, 4, 8, and 16. 5. **Largest common divisor**: The largest common divisor is 16. Thus, \( \operatorname{GCD}(16, 160) = 16 \). ### (c) \( \operatorname{GCD}(66, 0) \) 1. **Identify the numbers**: The numbers are 66 and 0. 2. **Definition of GCD with zero**: The GCD of any number \( a \) and 0 is defined as \( |a| \) (the absolute value of \( a \)), because any non-zero integer divides 0. 3. **Applying the definition**: Here, \( a = 66 \). Thus, \( \operatorname{GCD}(66, 0) = 66 \). ### Summary of Results: - (a) \( \operatorname{GCD}(60, 60) = 60 \) - (b) \( \operatorname{GCD}(16, 160) = 16 \) - (c) \( \operatorname{GCD}(66, 0) = 66 \)