1. **Problem Statement:** We are given that the product of the ages of three adults is 26390. We need to find the sum of their ages. 2. **Understanding the problem:** Each adult is at least 21 years old. We want to find three integers $a$, $b$, and $c$ such that: $$a \times b \times c = 26390$$ with $a, b, c \geq 21$. 3. **Step 1: Prime factorization of 26390** We start by factoring 26390 into prime factors: $$26390 \div 2 = 13195$$ $$13195 \div 5 = 2639$$ $$2639 \div 7 = 377$$ $$377 \div 13 = 29$$ $$29 \div 29 = 1$$ So the prime factorization is: $$26390 = 2 \times 5 \times 7 \times 13 \times 29$$ 4. **Step 2: Grouping factors into three numbers each at least 21** We want to group these primes into three factors $a$, $b$, and $c$ such that each is at least 21. Try grouping: - $a = 29$ (prime factor) - $b = 13 \times 2 = 26$ - $c = 7 \times 5 = 35$ Check if all are at least 21: - $29 \geq 21$ - $26 \geq 21$ - $35 \geq 21$ 5. **Step 3: Calculate the sum** $$a + b + c = 29 + 26 + 35 = 90$$ 6. **Answer:** The sum of their ages is **90**.