How do you find the greatest common factor of 30, 12?

Question

Skylar Adams · Accepted Answer

#GCF(12,30)=6#

First, split each number into their factors.

#30=1,2,3,5,6,10,15,30# #12=1,2,3,4,6,12#

Now we look for the greatest number appearing in both.

Both numbers have these factors: #1,2,3,6#

The greatest common factor will be the largest number in this list, which is #6#.

Emery Allen · Answer

undefined To find the greatest common factor (GCF) of 30 and 12, you can use several methods such as prime factorization, listing factors, or using the Euclidean algorithm. One commonly used method is prime factorization.

1. Prime factorize each number:
   - Prime factorization of 30: 30 = 2 × 3 × 5
   - Prime factorization of 12: 12 = 2 × 2 × 3

2. Identify the common prime factors and their minimum exponent:
   - Common prime factors: 2 and 3
   - Minimum exponent of 2: 2 (appears twice in the prime factorization of 12)
   - Minimum exponent of 3: 1 (appears once in the prime factorization of both 30 and 12)

3. Multiply the common prime factors with their minimum exponents:
   - GCF = 2^2 × 3^1 = 4 × 3 = 12

Therefore, the greatest common factor of 30 and 12 is 12.