Understanding Prime Factorization
Prime factorization is the process of expressing a number as a product of its prime factors. For the number 1323, we will break it down step by step.
Step 1: Dividing by the Smallest Prime
- Start with the smallest prime number, which is 2.
- Since 1323 is odd, it is not divisible by 2.
Step 2: Check for Divisibility by the Next Primes
- Check divisibility by 3:
- The sum of the digits (1 + 3 + 2 + 3 = 9) is divisible by 3.
- Divide 1323 by 3:
1323 ÷ 3 = 441
Step 3: Continue Factoring
- Now, factor 441:
- Again, check divisibility by 3:
441 ÷ 3 = 147
- Factor 147:
- Check divisibility by 3:
147 ÷ 3 = 49
Step 4: Factor 49
- Factor 49:
- Since 49 is not divisible by 3, check the next prime, which is 7:
49 ÷ 7 = 7
- Finally, factor 7:
- 7 is a prime number.
Step 5: Compile the Factors
- Now, compile all the factors found:
- 1323 = 3 × 3 × 3 × 7 × 7
- Simplifying this, we have:
- 1323 = 3^3 × 7^2
Final Prime Factorization
- The prime factorization of 1323 is:
- 3^3 × 7^2
This method effectively breaks down the number into its prime components, providing a clear understanding of its structure.