Is 1111 prime?
Understand the Problem
The question is asking whether the number 1111 is a prime number or not. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. To determine the primality of 1111, we will check if it can be divided evenly by any prime numbers less than or equal to the square root of 1111.
Answer
1111 is not a prime number.
Answer for screen readers
1111 is not a prime number.
Steps to Solve
- Calculate the square root of 1111
To determine the prime factors, we first find the square root of 1111. This helps us identify the range of prime numbers we need to check.
$$ \sqrt{1111} \approx 33.33 $$
We will check for prime divisors less than or equal to 33.
- List the prime numbers up to 33
The prime numbers less than or equal to 33 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31
- Check divisibility by each prime number
We will test each prime number from the list to see if it divides 1111 evenly.
- For 2: $1111 \div 2 = 555.5$ (not divisible)
- For 3: $1111 \div 3 \approx 370.33$ (not divisible)
- For 5: $1111 \div 5 = 222.2$ (not divisible)
- For 7: $1111 \div 7 \approx 158.71$ (not divisible)
- For 11: $1111 \div 11 = 101$ (divisible) Since 11 divides 1111 evenly, we conclude that it is not a prime number.
1111 is not a prime number.
More Information
Since 1111 can be expressed as a product of 11 and 101 (i.e., $1111 = 11 \times 101$), it has divisors other than 1 and itself, confirming it is not prime.
Tips
- Assuming a number is prime without checking all divisors thoroughly.
- Overlooking the need to check divisibility by all prime numbers up to the square root of the number.
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