Is 111 prime?
Understand the Problem
The question is asking whether the number 111 is a prime number. A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. To determine if 111 is prime, we would check for divisibility by other numbers.
Answer
111 is not prime.
Answer for screen readers
111 is not a prime number because it is divisible by 3.
Steps to Solve
- Check divisibility by 2
A prime number greater than 2 must be odd, so it should not be divisible by 2. Since 111 is odd, it is not divisible by 2.
- Check divisibility by numbers 3 to \sqrt{111}\ rounded up
We need to check if 111 is divisible by any prime numbers less than or equal to the square root of 111 (which is approximately 10.54). This means we need to check divisibility by 3, 5, and 7.
- Check divisibility by 3
A number is divisible by 3 if the sum of its digits is divisible by 3. The sum of the digits of 111 is 1 + 1 + 1 = 3, which is divisible by 3. Therefore, 111 is divisible by 3.
- Conclusion
Since 111 is divisible by 3, it has a positive divisor other than 1 and itself, which means it is not a prime number.
111 is not a prime number because it is divisible by 3.
More Information
The number 111 can be factored into 3 * 37.
Tips
A common mistake is to forget checking higher prime numbers up to the square root of the given number.
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