1. **State the problem:** Find the prime factorization of 1152. 2. **Recall the prime factorization method:** To find the prime factors of a number, divide it by the smallest prime number possible repeatedly until the quotient is 1. 3. **Start dividing 1152 by 2 (the smallest prime):** $$1152 \div 2 = 576$$ 4. **Continue dividing by 2:** $$576 \div 2 = 288$$ $$288 \div 2 = 144$$ $$144 \div 2 = 72$$ $$72 \div 2 = 36$$ $$36 \div 2 = 18$$ $$18 \div 2 = 9$$ 5. **Now 9 is not divisible by 2, move to the next prime, 3:** $$9 \div 3 = 3$$ $$3 \div 3 = 1$$ 6. **Count the number of times each prime divides 1152:** - 2 divides 7 times - 3 divides 2 times 7. **Write the prime factorization:** $$1152 = 2^{7} \times 3^{2}$$ This means 1152 is composed of seven 2's multiplied by two 3's. **Final answer:** $$1152 = 2^{7} \times 3^{2}$$