Question

learning goal 7.2: students will express composite whole numbers as a product of prime factors find the prime factorization of each value. 1. 275 2. 160 3. 232 4. 54

Explanation:

Step1: Prime Factorize 275

Start by dividing 275 by the smallest prime number, 5. \( 275 \div 5 = 55 \). Then divide 55 by 5 again: \( 55 \div 5 = 11 \). 11 is a prime number. So, \( 275 = 5 \times 5 \times 11 = 5^2 \times 11 \).

Step2: Prime Factorize 160

Divide 160 by 2: \( 160 \div 2 = 80 \). \( 80 \div 2 = 40 \), \( 40 \div 2 = 20 \), \( 20 \div 2 = 10 \), \( 10 \div 2 = 5 \). 5 is prime. So, \( 160 = 2 \times 2 \times 2 \times 2 \times 2 \times 5 = 2^5 \times 5 \).

Step3: Prime Factorize 232

Divide 232 by 2: \( 232 \div 2 = 116 \). \( 116 \div 2 = 58 \), \( 58 \div 2 = 29 \). 29 is prime. So, \( 232 = 2 \times 2 \times 2 \times 29 = 2^3 \times 29 \).

Step4: Prime Factorize 54

Divide 54 by 2: \( 54 \div 2 = 27 \). Then divide 27 by 3: \( 27 \div 3 = 9 \), \( 9 \div 3 = 3 \). 3 is prime. So, \( 54 = 2 \times 3 \times 3 \times 3 = 2 \times 3^3 \).

Answer:

1. \( 275 = 5^2 \times 11 \)
2. \( 160 = 2^5 \times 5 \)
3. \( 232 = 2^3 \times 29 \)
4. \( 54 = 2 \times 3^3 \)