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In Mathematics / College | 2025-07-07

What is the prime factorization of $96 ?$
A. $96=2 \times 2 \times 2 \times 2 \times 3$
B. $96=2 \times 2 \times 2 \times 2 \times 2 \times 3$
C. $96=2 \times 2 \times 2 \times 2 \times 2 \times 2$
D. $96=2 \times 2 \times 2 \times 12

Asked by zeezz19649

Answer (2)

Divide 96 by the smallest prime number, 2, repeatedly until you can't divide by 2 anymore.
Continue dividing by the next smallest prime number, 3, if necessary.
Express 96 as the product of all the prime factors found.
The prime factorization of 96 is 2 × 2 × 2 × 2 × 2 × 3 ​ .

Explanation

Understanding Prime Factorization We are asked to find the prime factorization of 96. This means we want to express 96 as a product of prime numbers. A prime number is a number greater than 1 that has only two factors: 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, and so on.

Step 1: Divide by 2 We can start by dividing 96 by the smallest prime number, 2. 96 ÷ 2 = 48 . So, 96 = 2 × 48 .

Step 2: Divide by 2 Now, we divide 48 by 2. 48 ÷ 2 = 24 . So, 96 = 2 × 2 × 24 .

Step 3: Divide by 2 Next, we divide 24 by 2. 24 ÷ 2 = 12 . So, 96 = 2 × 2 × 2 × 12 .

Step 4: Divide by 2 We divide 12 by 2. 12 ÷ 2 = 6 . So, 96 = 2 × 2 × 2 × 2 × 6 .

Step 5: Divide by 2 We divide 6 by 2. 6 ÷ 2 = 3 . So, 96 = 2 × 2 × 2 × 2 × 2 × 3 .

Final Prime Factorization Now we have expressed 96 as a product of prime numbers: 96 = 2 × 2 × 2 × 2 × 2 × 3 . This matches option B.


Examples
Prime factorization is a fundamental concept in number theory with various real-world applications. For instance, in cryptography, the security of many encryption algorithms relies on the difficulty of factoring large numbers into their prime factors. Imagine you have a lock with a combination, and the combination is a large number. If someone can quickly find the prime factors of that number, they can crack the code. This is why prime factorization is crucial in securing digital information and online transactions.

Answered by GinnyAnswer | 2025-07-08

The prime factorization of 96 is found by dividing it by 2 repeatedly until it cannot be divided anymore, yielding 2 5 × 3 . The correct option representing this factorization is B: 96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 .
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Answered by Anonymous | 2025-07-25

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