Is 539 prime?
Understand the Problem
The question is asking whether the number 539 is a prime number or not. A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In this case, we will check if 539 has any divisors other than 1 and itself.
Answer
539 is not a prime number.
Answer for screen readers
539 is not a prime number.
Steps to Solve
- Identify the definition of a prime number
A prime number has exactly two distinct positive divisors: 1 and itself. We need to check if 539 has any other divisors.
- Find the square root of 539
To determine if 539 is prime, we only need to check for factors up to its square root. Calculating the square root:
$$ \sqrt{539} \approx 23.2 $$
So we will check for divisibility using prime numbers up to 23.
- Check divisibility by prime numbers
We will check the prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, and 23.
- Divisibility by 2: 539 is odd, not divisible.
- Divisibility by 3: Sum of digits is $5 + 3 + 9 = 17$, not divisible.
- Divisibility by 5: Last digit not 0 or 5, not divisible.
- Divisibility by 7: $539 \div 7 = 77$, divisible.
Since 539 can be evenly divided by 7, it is not a prime number.
- Conclude the determination
Since we found a divisor other than 1 and 539, we conclude that 539 is not a prime number.
539 is not a prime number.
More Information
An interesting fact about 539 is that it can be expressed as the product of its prime factors: $539 = 7 \times 77$, and 77 can be further factored into $7 \times 11$. Therefore, the complete factorization is $539 = 7^2 \times 11$.
Tips
- Misunderstanding prime definition: Some may think that a prime number can have factors, but prime numbers can only have two divisors: 1 and itself.
- Not checking all primes: Failing to check all potential prime factors up to the square root can lead to incorrect conclusions.
