Understanding Prime Factorization
Prime factorization is the process of expressing a number as the product of its prime numbers. For the number 1323, we will systematically break it down into its prime factors.
Step 1: Check for Divisibility
- Begin with the smallest prime number, which is 2.
- Since 1323 is odd, it’s not divisible by 2.
Step 2: Test Higher Prime Numbers
- Next, try 3:
- Sum of the digits of 1323 (1+3+2+3=9) is divisible by 3.
- Dividing: 1323 ÷ 3 = 441
Step 3: Factor 441 Further
- Now, check 441 for prime factors.
- Again, sum of digits (4+4+1=9) shows it’s divisible by 3.
- Dividing: 441 ÷ 3 = 147
Step 4: Factor 147
- Check 147:
- Sum of digits (1+4+7=12) indicates divisibility by 3.
- Dividing: 147 ÷ 3 = 49
Step 5: Factor 49
- The number 49 is 7 multiplied by itself (7 x 7).
- Thus, 49 = 7².
Final Prime Factorization
- Bringing all factors together, we have:
- 1323 = 3 x 3 x 3 x 7 x 7
- This can be expressed as:
- 1323 = 3³ x 7²
In conclusion, the prime factorization of 1323 is 3³ x 7², showcasing the building blocks of this number.