Final answer:
The sum of the three prime numbers whose product is 646 is 38.
Step-by-step explanation:
The question asks for the sum of three prime numbers whose product is 646. To find the prime factors of 646, we start by finding a prime number that divides 646 without leaving a remainder. We find that 2, which is the smallest prime number, is a factor because 646 is an even number (it ends in 6). After dividing 646 by 2, we get 323. Next, we find that 323 can be divided by the prime number 17, giving us 19. Since 2, 17, and 19 are all prime numbers, and their product equals 646, we have found the required prime factors. The sum of these three prime numbers is 2 + 17 + 19 = 38.