What is the GCF of 6 and 8?
2
4
6
8
The greatest common factor (GCF) of 6 and 8 is 2. This simplest way to determine the GCF is through listing the factors of each number and identifying the largest number common to both lists. The factors of 6 are 1, 2, 3, and 6, while the factors of 8 are 1, 2, 4, and 8. The common factors are 1 and 2, with 2 being the highest, making it the GCF of 6 and 8. This method is straightforward and effective, especially for smaller numbers, providing a clear path to identifying the greatest common factor without the need for complex calculations or algorithms.
To find the greatest common factor (GCF) of 6 and 8 using the prime factorization method:
Step 1: Prime factorize both numbers:
For 6: 6 = 2 × 3
For 8: 8 = 2³
Step 2: Identify the common prime factors and their lowest powers:
The common prime factor between 6 and 8 is 2. The lowest power of 2 in the factorizations is 2¹.
Step 3: Multiply the common prime factors with their lowest powers to determine the GCF:
GCF = 2¹ = 2
Therefore, the greatest common factor (GCF) of 6 and 8 by the prime factorization method is 2.
To find the greatest common factor (GCF) of 6 and 8 using the long division method:
Step 1: Start by dividing the larger number (8) by the smaller number (6).
8 ÷ 6 =1 with a remainder of 2.
Step 2: Then, take the divisor (6) and divide it by the remainder (2).
6 ÷ 2 = 3 with a remainder of 0.
Since the remainder is now 0, the division process stops here.
Step 3: The divisors at this step, where the remainder becomes zero, is the greatest common factor (GCF).
GCF = 2.
Therefore, the greatest common factor (GCF) of 6 and 8 by the long division method is 2.
To find the greatest common factor (GCF) of 6 and 8 by listing common factors:
Step 1: List the factors of each number.
Factors of 6: 1, 2, 3, 6
Factors of 8: 1, 2, 4, 8
Step 2: Identify the common factors.
Common factors: 1, 2
Step 3: Determine the greatest common factor.
The highest number in the list of common factors is 2.
You can calculate the GCF using methods like prime factorization, listing common factors, or long division.
Long division and listing common factors are also effective methods.
Listing common factors might be the quickest for small numbers like these.
It breaks down numbers into their building blocks, revealing common factors.
Problems involving dividing or sharing quantities in ratios, simplifying algebraic fractions, and more.
Frequently in areas like engineering, computing, and when working with proportions.
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What is the GCF of 6 and 8?
2
4
6
8
Which of the following numbers is a common factor of 6 and 8?
1
3
4
6
What is the smallest number that is a multiple of both 6 and 8?
12
18
24
30
If you multiply the GCF of 6 and 8 by 3, what is the result?
6
9
12
18
Which of these is not a factor of 6 or 8?
2
3
5
6
What is the sum of the GCF of 6 and 8 and the LCM of 6 and 8?
20
18
30
36
What is the highest common factor of 6 and 8 if both numbers are increased by 2?
2
4
6
8
Which of the following pairs of numbers has the same GCF as 6 and 8?
10 and 15
12 and 18
20 and 30
14 and 21
What is the product of the GCF of 6 and 8 and 4?
8
12
16
24
Which of the following is a factor of both 6 and 8?
5
2
7
9
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