Is 65 prime or composite?
Understand the Problem
The question is asking whether the number 65 is a prime number or a composite number. A prime number is defined as a number greater than 1 that has no positive divisors other than 1 and itself, while a composite number has at least one positive divisor other than 1 and itself.
Answer
65 is a composite number.
Answer for screen readers
65 is a composite number.
Steps to Solve
- Identify the definition of prime and composite numbers
Recall that a prime number has only two distinct positive divisors: 1 and itself. A composite number has more than two positive divisors.
- Determine the factors of 65
To check if 65 is prime or composite, we need to find its divisors. We can start by checking for divisibility by smaller prime numbers, such as 2, 3, 5, and 7.
- Check divisibility by 2
65 is an odd number, so it is not divisible by 2.
- Check divisibility by 3
To check divisibility by 3, sum the digits of 65: $6 + 5 = 11$. Since 11 is not divisible by 3, 65 is not divisible by 3.
- Check divisibility by 5
The last digit of 65 is 5, which means it is divisible by 5. Therefore, we can divide:
$$ 65 \div 5 = 13 $$
- Conclude the factors
We found that 65 can be factored into $5 \times 13$. This means that 65 has divisors other than 1 and itself, specifically 5 and 13.
- Determine if 65 is prime or composite
Since 65 has more than two distinct positive divisors (1, 5, 13, and 65), it is classified as a composite number.
65 is a composite number.
More Information
Composite numbers are actually more common than prime numbers. The smallest prime number is 2, and every whole number greater than 1 is either a prime or composite.
Tips
One common mistake is assuming that any number that is not prime must be composite. Remember, both definitions should be considered: if a number has no divisors other than 1 and itself, it is prime; if it has additional divisors, it is composite.
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