What is the greatest common divisor (GCD) of 48 and 180?

To determine the greatest common divisor (GCD) of the numbers 48 and 180, we can utilize the method of prime factorization.

First, we find the prime factorization of each number:

• For 48:

• Divide 48 by 2: 48 ÷ 2 = 24

• Divide 24 by 2: 24 ÷ 2 = 12

• Divide 12 by 2: 12 ÷ 2 = 6

• Divide 6 by 2: 6 ÷ 2 = 3

• Finally, 3 is a prime number.

• Therefore, the prime factorization of 48 is ( 2^4 \times 3^1 ).

• For 180:

• Divide 180 by 2: 180 ÷ 2 = 90

• Divide 90 by 2: 90 ÷ 2 = 45

• Divide 45 by 3: 45 ÷ 3 = 15

• Divide 15 by 3: 15 ÷ 3 = 5

• Finally, 5 is a prime number