What is the prime factorization of $21 ?$
A. $21=21 \times 1$
B. $21=3 \times 5$
C. $21=3 \times 7$
D. $21=2 \times 2 \times 5$
Answer (2)
Prime factorization expresses a number as a product of its prime factors.
Check each option to see if it equals 21 and consists of prime numbers.
Option C, 21 = 3 × 7 , satisfies both conditions.
The prime factorization of 21 is 3 × 7 .
Explanation
Understanding Prime Factorization We are asked to find the prime factorization of 21 from the given options. Prime factorization means expressing a number as a product of its prime factors. A prime number is a number greater than 1 that has only two factors: 1 and itself.
Analyzing the Options Let's examine the options: A. 21 = 21 × 1 . This is not a prime factorization because 21 is not a prime number. B. 21 = 3 × 5 . Here, 3 and 5 are both prime numbers. However, 3 × 5 = 15 , not 21, so this is incorrect. C. 21 = 3 × 7 . Here, 3 and 7 are both prime numbers, and 3 × 7 = 21 . This is the correct prime factorization. D. 21 = 2 × 2 × 5 . Here, 2 and 5 are prime numbers. However, 2 × 2 × 5 = 20 , not 21, so this is incorrect.
Conclusion Therefore, the prime factorization of 21 is 3 × 7 .
Examples
Prime factorization is used in cryptography to secure data. For example, the security of the RSA algorithm relies on the fact that it is difficult to factor large numbers into their prime factors. In everyday life, understanding prime factors can help in simplifying fractions or finding the least common multiple when cooking or planning events.
The prime factorization of 21 is 3 × 7 , which consists of the prime numbers 3 and 7. The correct answer is option C: 21 = 3 × 7 .
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