What is the prime factorization for \( 100 ? \)

To find the prime factorization of \( 100 \), we can start by dividing it by the smallest prime number, which is \( 2 \). Since \( 100 \) is even, we can divide it by \( 2 \) to get \( 50 \). Continuing, we divide \( 50 \) by \( 2 \) again to get \( 25 \). Now, since \( 25 \) is not divisible by \( 2 \), we move to the next prime number, \( 3 \), but that doesn’t work either. Next, \( 5 \) is our star player. Dividing \( 25 \) by \( 5 \) gives us \( 5 \), and \( 5 \) divided by \( 5 \) is \( 1 \). So, the prime factorization of \( 100 \) is \( 2^2 \times 5^2 \). In real life, prime factorization helps in simplifying fractions, finding the greatest common divisor, and least common multiple of different numbers. It’s also incredibly useful in cryptography, where the difficulty of factoring large numbers into primes keeps our online transactions secure. So, while it seems like just a math trick, it’s a superhero in disguise that keeps our data safe!