Subjects number theory

Prime Check 523269

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1. **State the problem:** We are given the number 67 and need to understand or work with it as per the user's request. 2. **Since the user only provided the number 67 without a specific question, let's explore its properties:** 3. **Check if 67 is a prime number:** - A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. - Test divisibility by primes less than \(\sqrt{67} \approx 8.19\): 2, 3, 5, 7. - 67 is not divisible by 2 (it's odd). - Sum of digits is 6 + 7 = 13, not divisible by 3, so 67 is not divisible by 3. - Last digit is not 0 or 5, so not divisible by 5. - 67 divided by 7 is approximately 9.57, not an integer. 4. **Conclusion:** 67 has no divisors other than 1 and 67, so it is a prime number. **Final answer:** 67 is a prime number.