GCF of 8 and 6
GCF of 8 and 6
To find the Greatest Common Factor (GCF) of 8 and 6, list the factors of each numbers: the factors of 8 are 1, 2, 4, and 8, while the factors of 6 are 1, 2, 3, and 6. The common factors are 1 and 2, with the greatest common factor being 2. Therefore, the GCF of 8 and 6 is 2.
GCF of 8 and 6
GCF of 8 and 6 is 2.
Methods to Find GCF of 8 and 6
- Prime Factorization Method
- Long Division Method
- Listing Common Factors
GCF of 8 and 6 by Prime Factorization Method.
To find the Greatest Common Factor (GCF) of 8 and 6 using the prime factorization method, follow these steps:
Step 1: Find the prime factorization of each number
Prime factorization of 8:
8 = 2 × 2 × 2 = 2³
Prime factorization of 6:
6 = 2 × 3
Step 2: Identify the common prime factors
The common prime factor of 8 and 6 is 2.
Step 3: Multiply the common prime factors
Since the only common prime factor is 2, the GCF is 2.
GCF of 8 and 6 by Long Division Method.
To find the Greatest Common Factor (GCF) of 8 and 6 using the long division method, follow these steps:
Step 1: Divide the larger number by the smaller number
8 ÷ 6 = 1 with a remainder of 2.
Step 2: Replace the larger number with the smaller number, and the smaller number with the remainder
Now, we have 6 and 2.
Step 3: Repeat the division
6 ÷ 2 = 3 with a remainder of 0.
Step 4: When the remainder is 0, the divisors is the GCF
The last non-zero remainder is 2. So, the GCF of 8 and 6 is 2.
GCF of 8 and 6 by Listing Common Factors.
To find the Greatest Common Factor (GCF) of 8 and 6 by listing common factors, follow these steps:
Step 1: List the factors of each number
Factors of 8:
- 1, 2, 4, 8
Factors of 6:
- 1, 2, 3, 6
Step 2: Identify the common factors
Common factors of 8 and 6:
- 1, 2
Step 3: Determine the greatest common factor
The largest common factor is 2. Therefore, the GCF of 8 and 6 is 2.
How are the GCF and LCM of two numbers related?
The product of the GCF and LCM of two numbers equals the product of the numbers.
Can the GCF of two numbers ever be one of the numbers?
Yes, if one number is a multiple of the other. For example, the GCF of 2 and 6 is 2.
Can the GCF of 8 and 6 be used to simplify the fraction 8/6?
Yes, simplifying 8/6 using the GCF of 2 gives 4/3.
Can the GCF of 8 and 6 be greater than 2?
No, 2 is the greatest common factor of 8 and 6.
How do you find the GCF of 8 and 6?
You can find the GCF by using methods such as listing common factors, prime factorization, and the long division method.
How do you explain the GCF to someone learning it for the first time?
Describe it as the largest number that can divide two or more numbers without leaving a remainder. For 8 and 6, that number is 2.
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