Questions Express 72 as a product of its prime factors.

To express 72 as a product of its prime factors, we start by dividing by the smallest prime number, which is 2. So, we divide: 72 ÷ 2 = 36, then again 36 ÷ 2 = 18, and again 18 ÷ 2 = 9. Now, 9 isn’t divisible by 2, so we move to the next prime number, 3: 9 ÷ 3 = 3, and finally 3 ÷ 3 = 1. This gives us the prime factorization of 72 as: 2 × 2 × 2 × 3 × 3, which can be written as \(2^3 \times 3^2\). Prime numbers are the building blocks of other numbers, and breaking down a number like 72 into its prime factors can be quite handy! It's particularly useful in various real-world applications like cryptography, computing, and even in your kitchen when you need to find the right measurements for recipes! Understanding the composition of numbers helps in simplifying complex problems or calculations in a fun, systematic way!