Which of the following is a composite number?
A. 29
B. 13
C. 139
D. 91
Answer (2)
A composite number has factors other than 1 and itself.
Check each option: 29, 13, and 139 are prime.
91 is divisible by 7 and 13 ( 91 = 7 × 13 ).
Therefore, the composite number is 91 .
Explanation
Understanding Composite Numbers A composite number is a positive integer that has at least one positive divisor other than one or itself. We need to identify which of the given numbers (29, 13, 139, 91) is composite.
Checking Each Number Let's check each number:
29: The only factors of 29 are 1 and 29. Therefore, 29 is a prime number.
13: The only factors of 13 are 1 and 13. Therefore, 13 is a prime number.
139: The only factors of 139 are 1 and 139. Therefore, 139 is a prime number.
91: We can observe that 91 = 7 × 13 . Therefore, 91 has factors other than 1 and itself (7 and 13), making it a composite number.
Identifying the Composite Number Therefore, the composite number among the given options is 91.
Final Answer The answer is D. 91
Examples
Understanding composite numbers is crucial in cryptography, where the security of encryption methods often relies on the difficulty of factoring large composite numbers into their prime factors. For instance, the RSA algorithm, widely used for secure data transmission, depends on the fact that it's easy to multiply two large prime numbers but very hard to factor the result back into the original primes. Knowing that 91 is composite (7 * 13) helps illustrate how a seemingly large number can be easily broken down, highlighting the importance of using much larger prime numbers in real-world encryption.
The composite number among the options is 91, as it can be divided by factors other than 1 and itself (specifically 7 and 13). The other numbers, 29, 13, and 139, are all prime numbers. Therefore, the correct answer is D. 91.
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