Question

example carly is asked to find the prime factorization of 60. she decides to make a factor tree. 60 2 30 2 15 2 2 3 5 carly writes the prime factorization of 60 as 2·2·3·5. 1 rewrite carlys solution using exponents. 2 find the prime factorization of 60 using the division by least prime number method. circle all prime numbers. write your answer using exponents. show your work.

Explanation:

Step1: Identify repeated prime factors

Carly's prime - factorization is 2×2×3×5. The factor 2 is repeated twice.

Step2: Rewrite using exponents

For the repeated factor 2, we can write it as 2². So the prime - factorization of 60 using exponents is 2²×3×5.

Step3: Prime - factorize 60 using division by least prime number

Start with 60. The least prime number is 2. 60÷2 = 30. Then 30÷2 = 15. Then 15÷3 = 5. Since 5 is a prime number, we stop. The prime - factors are 2, 2, 3, 5.

Step4: Write the answer using exponents

The prime - factorization of 60 using exponents is 2²×3×5.

Answer:

1. 2²×3×5
2. Work: 60÷2 = 30, 30÷2 = 15, 15÷3 = 5. Prime - factorization: 2²×3×5