Final answer:
The prime factorization of the number 100 is found by repeatedly dividing by prime numbers, resulting in 100 = 22 x 52.
Step-by-step explanation:
To determine the prime factorization of the number 100, we need to break it down into prime numbers that multiply together to give us 100. We start by dividing 100 by the smallest prime number, which is 2. Since 100 is even, we know it is divisible by 2.100 ÷ 2 = 50. Now, we divide 50 by 2 again, which gives us 25. Since 25 is not divisible by 2, we move on to the next prime number, which is 3. However, 25 is not divisible by 3 either, so we move on to the next prime number, 5.
25 ÷ 5 = 5. Finally, since 5 is a prime number, we have reached the end of our factorization. We can now express 100 as a product of prime factors: 100 = 2 x 2 x 5 x 5, or in exponential form, 100 = 22 x 52. The process of prime factorization is important in various areas of mathematics, including simplifying fractions, finding least common multiples, and working with exponents.