Final answer:
To find the integers a and b such that GCD(a,b) = 3 and a*b = 65, you can factor 65 into its prime factors and multiply them by 3 to get the numbers a and b.
Step-by-step explanation:
GCD stands for Greatest Common Divisor, which is the largest positive integer that divides both numbers without leaving a remainder. To find the integers a and b such that GCD(a,b) = 3, we need to find two numbers whose GCD is 3. To find two numbers that multiply to give 65, we can start by factoring 65 into its prime factors: 65 = 5 * 13. Since the GCD of two numbers is the product of their common prime factors, the two numbers can be written as a = 3 * 5 = 15 and b = 3 * 13 = 39. Therefore, the integers a and b such that GCD(a,b) = 3 and a*b = 65 are 15 and 39.