What is the prime factorization of 4?
A. [tex]$4=2 \times 2$[/tex]
B. [tex]$4=2 \times 4$[/tex]
C. [tex]$4=2 \times 2 \times 2$[/tex]
D. [tex]$4=4 \times 1$[/tex]
Answer (2)
Prime factorization means expressing a number as a product of its prime factors.
Divide 4 by the smallest prime number, 2, which gives 2.
Since 2 is a prime number, the prime factorization of 4 is 2 × 2 .
The correct option is 4 = 2 × 2 .
Explanation
Understanding Prime Factorization We are asked to find the prime factorization of 4. This means we need to express 4 as a product of its prime factors. 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.
Finding Prime Factors We can start by dividing 4 by the smallest prime number, 2. 4 o b re ak ÷ 2 = 2 . Since 2 is also a prime number, we have found the prime factors of 4.
Expressing as a Product of Prime Factors Therefore, the prime factorization of 4 is 2 × 2 .
Comparing with Options Now, we compare our result with the given options: A. 4 = 2 × 2 B. 4 = 2 × 4 C. 4 = 2 × 2 × 2 D. 4 = 4 × 1 Option A matches our result.
Final Answer The prime factorization of 4 is 4 = 2 × 2 .
Examples
Prime factorization is a fundamental concept in number theory and has many real-world applications. For example, when designing secure communication systems, prime factorization is used in cryptography to create encryption keys. The security of these systems relies on the fact that it is computationally difficult to factor large numbers into their prime factors. Another application is in simplifying fractions. By finding the prime factors of the numerator and denominator, you can cancel out common factors and reduce the fraction to its simplest form.
The prime factorization of 4 is expressed as 4 = 2 × 2 . Therefore, the correct option is A. This means that 4 is made up of two prime factors, which are both 2.
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