MATH SOLVE

2 months ago

Q:
# Prime factorization of 48?

Accepted Solution

A:

Answer: 2 x 2 x 2 x 2 x 3Step-by-step explanation: To find the prime factorization of 48, first create a factor tree with two branches.When a number is even, it's often easiest to start by dividing by 2 to find factors.Since 48 ÷ 2 . is 24, we know that 2 and 24 are factors of 48 so we write 2 and 24 at the bottom of the branches.Next, we circle any prime factors in the factor tree. Since 2 is classified as a prime number, we circle 2 but since 24 is not a prime number, we draw two new branches.Since 24 ÷ 2 is 12, we know that 2 and 12 are factors of 24 so we write 2 and 12 at the bottom of the branches.Next, we circle any prime factors in the factor tree. Since 2 is classified as a prime number, we circle 2. Since 12 is not a prime number, we draw two new branches.Since 12 ÷ 2 is 6, we know that 2 and 6 are factors of 12. This means that we write 2 and 6 at the bottom of the branches. Next, we circle any prime factors in the factor tree. Since 2 is a prime number, we circle 2 but draw two new branches coming down from 6 because it's not prime.Since 6 ÷ 2 is 3, we know that 2 and 3 are factors of 6 so we write 2 and 3 at the bottom of the branches. Next, we circle any prime factors in the factor tree. Since both 2 and 3 are prime meaning that the only factors they have are 1 and the number itself, we circle both 2 and 3. Since we have circles at the bottom of all of the branches, we are finished.So the prime factorization of 48 is 2 × 2 × 2 × 2 × 3.Notice that the factor 2 is repeated 4 times. In this case, we can rewrite the prime factorization of 48 using exponents as [tex]2^{4}[/tex] x 3