what is the gcd of 80 and 100

Answer 1

To find the greatest common divisor (gcd) of 80 and 100, we can use the prime factorization method:

1. Prime factorization of 80:

   • 80 = 2 × 40
   • 40 = 2 × 20
   • 20 = 2 × 10
   • 10 = 2 × 5
   • So, the prime factorization of 80 is: \( 80 = 2^4 × 5^1 \).

2. Prime factorization of 100:

   • 100 = 10 × 10
   • 10 = 2 × 5
   • So, \( 100 = 2^2 × 5^2 \).

3. Finding the gcd:

   • For each prime factor, take the lowest power that appears in both factorizations:
     • For the prime \(2\): the minimum power is \(2^2\).
     • For the prime \(5\): the minimum power is \(5^1\).

4. Calculating the gcd:

   • The gcd = \(2^2 × 5^1 = 4 × 5 = 20\).

Thus, the gcd of 80 and 100 is 20.