8.7. Greatest Common Divisor (GCD)

Try these first

1. 1.

   What is the GCD of 10 and 25?

   Hint

   Find the largest number that divides both.

2. 2.

   Name two co-prime numbers.

   Hint

   Look for numbers that share no divisors other than 1.

3. 3.

   What does GCD stand for?

   • Greatest Common Divisor
   • Greatest Common Denominator
   • General Common Divisor

   Hint

   Recall its definition.

4. 4.

   True or False: If the GCD of two numbers is greater than 1, they are co-prime.

   • True
   • False

   Hint

   Think about the definition of co-primality.

5. 5.

   Prove that the GCD of any number and 0 is the number itself.

   Hint

   Consider how division works.

6. 6.

   Employ Lame's theorem to find the GCD of two very large numbers, illustrating the process of using it.

   Hint

   Track the remainders and relate them to the Fibonacci sequence.