greatest common factor of 105, 30, and 60
To find the greatest common factor (GCF) of 105, 30, and 60, we can start by listing the prime factors of each number:
105 = 3 x 5 x 7
30 = 2 x 3 x 5
60 = 2 x 2 x 3 x 5
Now we can find the common factors by looking at the shared prime factors. Each number has 2 and 3 in common. So, the GCF of 105, 30, and 60 is 2 x 3, which equals 6.
To find the greatest common factor (GCF) of 105, 30, and 60, we can begin by finding the prime factorization of each number.
The prime factorization of 105 is 3 × 5 × 7.
The prime factorization of 30 is 2 × 3 × 5.
The prime factorization of 60 is 2 × 2 × 3 × 5.
Now, let's identify the common prime factors in all three numbers and multiply them together to find the GCF.
The common prime factors are 3 and 5. Multiplying them together: 3 × 5 = 15.
Therefore, the greatest common factor of 105, 30, and 60 is 15.
To find the greatest common factor (GCF) of three numbers, you can use either prime factorization or the method of listing factors. Let's use prime factorization.
Step 1: Prime factorize each of the three numbers separately.
- Prime factorization of 105: 3 × 5 × 7
- Prime factorization of 30: 2 × 3 × 5
- Prime factorization of 60: 2 × 2 × 3 × 5
Step 2: Identify the common prime factors among the three numbers. In this case, the common prime factors are 3 and 5.
Step 3: Multiply the common prime factors to find the GCF. In this case, the GCF is 3 × 5 = 15.
Therefore, the greatest common factor (GCF) of 105, 30, and 60 is 15.
Note: If you prefer the method of listing factors, you can list the factors of each number and find the common factors manually. However, prime factorization is usually more efficient when dealing with larger numbers.