What is the G.C.D of 12,28 and 49
The GCD (Greatest Common Divisor) of 12, 28, and 49 is 1.
To find the greatest common divisor (G.C.D) of 12, 28, and 49, we can use the method of factorization.
Step 1: Prime factorization of each number:
- 12 = 2^2 * 3
- 28 = 2^2 * 7
- 49 = 7^2
Step 2: Identify the common prime factors:
- The common prime factor between 12 and 28 is 2^2 = 4.
- There are no common prime factors between the previous result (4) and 49.
Step 3: Multiply the common prime factors:
- The G.C.D of 12, 28, and 49 is 4.
Therefore, the G.C.D of 12, 28, and 49 is 4.
To find the greatest common divisor (G.C.D) of three numbers, we can use the factorization method. First, let's find the prime factors of each number:
1. Number: 12
- Prime factors: 2, 2, 3 (12 = 2 * 2 * 3)
2. Number: 28
- Prime factors: 2, 2, 7 (28 = 2 * 2 * 7)
3. Number: 49
- Prime factors: 7, 7 (49 = 7 * 7)
Now, we identify the common prime factors among all three numbers, along with their common highest exponent:
- 2: appears in the prime factorization of 12 and 28, highest exponent = 2
- 7: appears in the prime factorization of 28 and 49, highest exponent = 1
To find the G.C.D, we multiply the common prime factors with their common highest exponent:
G.C.D = 2^2 * 7^1 = 4 * 7 = 28
Therefore, the G.C.D of 12, 28, and 49 is 28.