To find the prime factorization of 375, we start by dividing the number by the smallest prime number, which is 2. Since 375 is an odd number, it cannot be divided by 2.
Next, we try dividing by 3. The sum of the digits of 375 (3 + 7 + 5 = 15) is divisible by 3, so we can divide:
- 375 ÷ 3 = 125
Now we have 125. Again, we check if it can be divided by 3. The sum of the digits of 125 (1 + 2 + 5 = 8) is not divisible by 3, so we move to the next prime number, which is 5:
- 125 ÷ 5 = 25
We can factor 25 further:
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1
Now, putting it all together, we see that:
- 375 = 3 × 5 × 5 × 5
- This can also be written as 375 = 3 × 5³
Therefore, the prime factorization of 375 is 3 × 5³.