What is the prime factorization of 288 write your answer using exponents

Answer 1

To find the prime factorization of 288, we can divide the number by prime numbers:

1. Start with 288: \[ 288 \div 2 = 144 \]
2. Divide 144 by 2: \[ 144 \div 2 = 72 \]
3. Divide 72 by 2: \[ 72 \div 2 = 36 \]
4. Divide 36 by 2: \[ 36 \div 2 = 18 \]
5. Divide 18 by 2: \[ 18 \div 2 = 9 \]
6. Now divide 9 by 3: \[ 9 \div 3 = 3 \]
7. Finally, divide 3 by 3: \[ 3 \div 3 = 1 \]

Now we can summarize the divisions. The number 288 can be expressed in terms of its prime factors: \[ 288 = 2^5 \times 3^2 \]

So, the prime factorization of 288 is: \[ 2^5 \times 3^2 \]