what is the prime number of 65
The correct answer and explanation is:
The number 65 itself is not a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, a prime number can only be divided evenly (without leaving a remainder) by 1 and the number itself.
To determine if 65 is prime, check whether it has divisors other than 1 and 65. The factors of 65 are:
- 1 and 65 (since every number is divisible by 1 and itself),
- 5 and 13, because 5 × 13 = 65.
Since 65 can be divided evenly by 5 and 13, it is a composite number, meaning it is not prime.
Prime numbers are the building blocks of all natural numbers because any number can be expressed as a product of prime numbers. This is known as the Fundamental Theorem of Arithmetic.
To clarify further, numbers like 2, 3, 5, 7, 11, 13, 17, and so on are prime numbers. They only have two factors, themselves and 1. Composite numbers like 4, 6, 8, 9, 10, 12, and 65 have more than two factors.
In the case of 65, the prime factors are 5 and 13. Both 5 and 13 are prime numbers because:
- 5 is only divisible by 1 and 5,
- 13 is only divisible by 1 and 13.
Finding the prime factors of a number helps in many areas of mathematics including simplifying fractions, finding greatest common divisors, and least common multiples.
To summarize, 65 is not prime. Instead, it is a composite number with prime factors 5 and 13.