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Is a prime number or a composite number? Choices: (A) prime number (B) composite number
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Q. Is a prime number or a composite number? Choices: (A) prime number (B) composite number
- Definition of Prime and Composite Numbers: A prime number is a number greater than that has no positive divisors other than and itself. A composite number is a number that has at least one positive divisor other than and itself. To determine if is a prime number or a composite number, we need to check if it has any divisors other than and .
- Check Divisibility by Prime Numbers: We start by checking if is divisible by any prime number less than or equal to the square root of . The square root of is approximately , so we only need to check for divisibility by the prime numbers , , and .
- Check Divisibility by : First, check if is divisible by . Since is an odd number, it is not divisible by .
- Check Divisibility by : Next, check if is divisible by . The sum of the digits of () is , which is not divisible by . Therefore, is not divisible by .
- Check Divisibility by : Finally, check if is divisible by . Any number that ends with a or is divisible by , and since does not end with a or , it is not divisible by .
- Conclusion: is a Prime Number: Since is not divisible by any prime number less than or equal to its square root, it has no divisors other than and itself. Therefore, is a prime number.
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