A A.eks ALEKS - Dixie Flores - Learn Ellucian Ethos Identity Cont Arithmotic Readiness Prime factorization Write 48 as a product of prime factors. \[ 48= \] \( \square \) \( \square \) \[ 1 \times \square \] Explanation Check

To write 48 as a product of prime factors, we can start by dividing 48 by the smallest prime number, which is 2. This gives us: \[ 48 \div 2 = 24 \] Continuing this process: \[ 24 \div 2 = 12 \\ 12 \div 2 = 6 \\ 6 \div 2 = 3 \\ 3 \div 3 = 1 \] So when we put this together, we get: \[ 48 = 2^4 \times 3^1 \] Each time we divided by a prime number until we reached 1, we effectively used all of the prime factors. For the "check" part, we can multiply the prime factors back together: \[ 2 \times 2 \times 2 \times 2 \times 3 = 48 \] And voila! The prime factorization is confirmed: \[ 48 = 2 \times 2 \times 2 \times 2 \times 3 \] or in exponential form: \[ 48 = 2^4 \times 3^1 \]