1. The problem asks: Why 54? We interpret this as understanding the number 54 in a mathematical context. 2. Let's explore the properties of 54. 3. 54 is a composite number. It can be factored into prime factors using the formula for prime factorization. 4. Prime factorization means expressing 54 as a product of prime numbers. 5. Start dividing 54 by the smallest prime number 2: $$54 \div 2 = 27$$ 6. Since 27 is not divisible by 2, try the next prime number 3: $$27 \div 3 = 9$$ 7. Continue dividing 9 by 3: $$9 \div 3 = 3$$ 8. Finally, divide 3 by 3: $$3 \div 3 = 1$$ 9. So, the prime factorization of 54 is: $$54 = 2 \times 3 \times 3 \times 3 = 2 \times 3^3$$ 10. This means 54 is made up of one 2 and three 3s multiplied together. 11. Understanding prime factorization helps in simplifying fractions, finding greatest common divisors, and least common multiples. 12. Therefore, 54 is significant as a product of primes 2 and 3 cubed.