what is the GCD of three consecutive numbers?
Answers
Answer:
The greatest common divisor of any two consecutive integers is 1, it follows that the GCD of three consecutive numbers is also 1. Therefore, for any three consecutive integers n, n+1, and n+2, the greatest common divisor is always 1.
Explanation:
To find the greatest common divisor (GCD) of three consecutive numbers, we can use the fact that any two consecutive integers are always coprime, meaning they have no common divisors other than 1.
Suppose the three consecutive numbers are n, n+1, and n+2. We can begin by finding the GCD of the first two numbers, n and n+1. Since these two numbers are consecutive, they are coprime. Therefore, their GCD is 1.
Next, we find the GCD of the second and third numbers, (n+1) and (n+2). By observing that (n+2) - (n+1) = 1, we see that (n+1) and (n+2) are also consecutive integers and therefore coprime. Hence, their GCD is also 1.
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