Write 1,386 as the product of its prime factors. A) \( 2 \times 693 \) B) \( 2 \times 3 \times 231 \) C) \( 2 \times 3 \times 3 \times 7 \times 11 \) D) \( 2 \times 3 \times 7 \times 33 \)

To factor 1,386 into its prime factors, we can start by dividing it by the smallest prime numbers. 1. **Divide by 2** (the smallest prime): \[ 1386 \div 2 = 693 \] So, we have: \[ 1386 = 2 \times 693 \] 2. **Next, factor 693**. We can check if it is divisible by 3: \[ 693 \div 3 = 231 \] So, we have: \[ 693 = 3 \times 231 \] Thus: \[ 1386 = 2 \times 3 \times 231 \] 3. **Now, factor 231**. Check if it is divisible by 3 again: \[ 231 \div 3 = 77 \] So, we have: \[ 231 = 3 \times 77 \] Thus: \[ 1386 = 2 \times 3 \times 3 \times 77 \] 4. **Next, factor 77**. It is divisible by 7: \[ 77 \div 7 = 11 \] So, we have: \[ 77 = 7 \times 11 \] Thus: \[ 1386 = 2 \times 3 \times 3 \times 7 \times 11 \] Now we can write the complete prime factorization: \[ 1386 = 2 \times 3^2 \times 7 \times 11 \] Looking at the options provided: - A) \( 2 \times 693 \) - B) \( 2 \times 3 \times 231 \) - C) \( 2 \times 3 \times 3 \times 7 \times 11 \) - D) \( 2 \times 3 \times 7 \times 33 \) The correct answer is: **C) \( 2 \times 3 \times 3 \times 7 \times 11 \)**.