To find the prime factorization of 250, we need to break it down into its prime factors. Here are the steps:
1. Start with the smallest prime number, which is 2.
- Check if 250 is divisible by 2.
- Since 250 is even, it is divisible by 2. Divide 250 by 2 to get 125.
- So, 2 is one of the prime factors, and we now have 125 left to factorize.
2. Move to the next smallest prime number, which is 3.
- Check if 125 is divisible by 3.
- Add the digits of 125: [tex]\(1 + 2 + 5 = 8\)[/tex]. Since 8 is not divisible by 3, 125 is not divisible by 3.
3. Move to the next prime number, which is 5.
- Check if 125 is divisible by 5.
- Since 125 ends in a 5, it is divisible by 5. Divide 125 by 5 to get 25.
- So, 5 is one of the prime factors, and we now have 25 left to factorize.
4. Continue with 5, since 25 is still divisible by 5.
- Divide 25 by 5 to get 5.
- 5 is again a prime factor.
- Finally, 5 divided by 5 gives us 1, so we are done with the factorization.
The prime factors of 250 are:
[tex]\[2, 5, 5, 5\][/tex]
When ordered from least to greatest, the prime factorization of 250 is:
[tex]\[
2 \times 5 \times 5 \times 5
\][/tex]
