Use a factor tree to find the prime factorization of 96. Write the prime factorization using exponents.
A. 23 • 62
B. 25 • 42
C. 25 • 3
D. 3 • 52
96 = 32*3 = 2^5 * 3^1
What is the prime factorization of 100?
A
22 × 52
B
25 × 2
C
5 × 2
D
22 × 52
To find the prime factorization of a number, you can use a factor tree. Here's how you can find the prime factorization of 96:
Step 1: Divide 96 by any prime factor. Let's start with the smallest prime number, 2. 96 ÷ 2 = 48.
Step 2: Now, continue dividing the quotient (48) by a prime factor until you can no longer divide.
48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
Step 3: We have reached a prime number (3) which cannot be further divided. So, the prime factorization of 96 is: 2 × 2 × 2 × 2 × 2 × 3.
Now, we can rewrite this using exponents: 2^5 × 3.
Looking at the answer choices provided:
A. 23 • 62
B. 25 • 42
C. 25 • 3
D. 3 • 52
The correct prime factorization using exponents for 96 is option D: 3 • 52.