What is the GCF of two different prime numbers? Explain ur reasoning.
a prime n has only two factors: 1 and n
distinct primes have no common factors other than 1.
so, 1 = GCF
Use the definition of a prime number.
http://www.mathsisfun.com/prime_numbers.html
The GCF (Greatest Common Factor) of two different prime numbers is always 1. This is because prime numbers have only two factors, 1 and themselves.
To determine the GCF of two prime numbers, you can follow these steps:
1. Identify the prime numbers: Start by identifying the two different prime numbers. Remember, prime numbers are natural numbers greater than 1 that are only divisible by 1 and themselves. Examples of prime numbers are 2, 3, 5, 7, 11, and so on.
2. List the factors: List the factors of each prime number. Since prime numbers only have two factors, the lists will be short. For instance, the factors of 2 are only 1 and 2, and the factors of 3 are only 1 and 3.
3. Find the common factors: Compare the lists of factors for both prime numbers and determine the common factors. Since prime numbers only have two factors, the only common factor between them will always be 1.
4. Determine the GCF: The GCF is the greatest common factor, which in this case is 1. Since 1 is the only common factor between two different prime numbers, it is the highest (greatest) common factor.
So, 1 is the GCF of any two different prime numbers because it is the only factor they have in common.