Final answer:
To find the prime factorization of 1,925, divide it by the smallest prime numbers until the result can no longer be divided. The prime factorization of 1,925 is 2 × 2 × 3 × 2 × 2 × 2 × 2 × 5.
Step-by-step explanation:
To find the prime factorization of 1,925, we need to factorize it into its prime factors. We start by dividing it by the smallest prime number, which is 2. 1,925 divided by 2 gives us 962 remainder 1. Since 962 is an even number, we continue dividing by 2 until we can't anymore. So, 1,925 can be written as 2 × 2 × 481. Then, we divide 481 by the smallest prime number, which is 3. 481 divided by 3 gives us 160 remainder 1. Continuing this process, we find that 1,925 can be expressed as 2 × 2 × 3 × 160. Finally, we break down 160 into its prime factors, which are 2 × 2 × 2 × 2 × 5. Therefore, the prime factorization of 1,925 is 2 × 2 × 3 × 2 × 2 × 2 × 2 × 5.