what is the gcf of 54,144

factors of 54 : 2,3,9,27

factors of 144 : 2,3,4 ..........

which is the largest belonging to both ?

Gcf 54,144

To find the greatest common factor (GCF) of 54 and 144, we can use the following steps:

Step 1: List the factors of 54: 1, 2, 3, 6, 9, 18, 27, 54.
Step 2: List the factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.
Step 3: Find the common factors in both lists: 1, 2, 3, 6, 9, 18.
Step 4: Identify the greatest common factor from the common factors list: 18.

Therefore, the GCF of 54 and 144 is 18.

To find the greatest common factor (GCF) of 54 and 144, you can use a method called prime factorization.

Step 1: Prime factorize the numbers 54 and 144.
- Start by dividing each number by the smallest prime number, which is 2.
- Keep dividing until you can no longer divide evenly.

The prime factorization of 54: 2 × 3 × 3 × 3 = 2 × 3^3
The prime factorization of 144: 2 × 2 × 2 × 2 × 3 × 3 = 2^4 × 3^2

Step 2: Identify the common factors.
- Look for the prime factors that are common to both numbers.
- In this case, the only common prime factor is 2, raised to the power of 2.

Step 3: Calculate the GCF.
- Multiply the common factors.
- The GCF is 2 × 2 = 4.

Therefore, the greatest common factor (GCF) of 54 and 144 is 4.