Understanding Prime Factorization
Prime factorization is the process of breaking down a composite number into its prime factors. Prime numbers are numbers greater than 1 that have no positive divisors other than 1 and themselves.
Step-by-Step Prime Factorization of 550
1. Start with the Number
- Begin with the number 550.
2. Divide by the Smallest Prime
- Check for divisibility by the smallest prime number, which is 2.
- Since 550 is even, divide by 2.
- 550 ÷ 2 = 275.
3. Continue with the Next Prime
- Now, check 275 for divisibility by the next smallest prime, which is 3.
- 275 is not divisible by 3. Move to the next prime, which is 5.
- 275 ÷ 5 = 55.
4. Factor Further
- Now, take 55 and check for divisibility.
- 55 is divisible by 5 again.
- 55 ÷ 5 = 11.
5. Identify the Remaining Prime
- The last number, 11, is a prime number itself.
Final Prime Factorization
Putting it all together, the prime factorization of 550 can be expressed as:
- 2 x 5 x 5 x 11
- Or, in exponential form: 2 x 5² x 11.
This breakdown shows that 550 is composed of the prime factors 2, 5 (twice), and 11. Understanding this helps in various mathematical applications, including simplifying fractions and finding the greatest common divisor.