GCF of 6 and 18
GCF of 6 and 18
The greatest common factor (GCF) of 6 and 18 is 6. This is determined by identifying the largest number that both numbers can be divided by without leaving a remainder. You can find the GCF through several methods, including listing the factors of each number, using prime factorization, or applying the Euclidean algorithm. Factors of 6 are 1, 2, 3, and 6, while factors of 18 are 1, 2, 3, 6, 9, and 18. The highest common factor between these is 6, making it the GCF. This method of listing factors is straightforward and provides a quick way to determine the greatest common divisor for smaller numbers like 6 and 18.
GCF of 6 and 18
GCF of 6 and 18 is 6.
GCF of 6 and 18 by Prime Factorization Method.
To find the greatest common factor (GCF) of 6 and 18 using the prime factorization method:
Step 1: Prime factorize both numbers:
For 6: 6 = 2 × 3
For 18: 18 = 2 × 3²
Step 2: Identify the common prime factors and their lowest powers:
Both 6 and 18 have the common prime factors of 2 and 3. The lowest power of each is 2¹ and 3¹.
Step 3: Multiply the common prime factors with their lowest powers to determine the GCF: GCF = 2¹ × 3¹ = 2 × 3 = 6
Therefore, the greatest common factor (GCF) of 6 and 18 by the prime factorization method is 6.
GCF of 6 and 18 by Long Division Method.
To find the greatest common factor (GCF) of 6 and 18 using the long division method:
Step 1: Start by dividing the larger number (18) by the smaller number (6).
18 ÷ 6 = 3 with a remainder of 0.
Since the remainder is now 0, the division process stops here.
Step 2: The divisors at this step where the remainder becomes zero is the greatest common factor (GCF).
GCF = 6.
Therefore, the greatest common factor (GCF) of 6 and 18 by the long division method is 6.
GCF of 6 and 18 by Listing Common Factors.
To find the greatest common factor (GCF) of 6 and 18 by listing common factors:
Step 1: List the factors of each number.
Factors of 6: 1, 2, 3, 6
Factors of 18: 1, 2, 3, 6, 9, 18
Step 2: Identify the common factors.
The common factors that 6 and 18 share are: 1, 2, 3, 6
Step 3: Determine the greatest common factor.
The largest number among the common factors is 6.
Therefore, the greatest common factor (GCF) of 6 and 18 by listing common factors is 6.
Does the GCF of 6 and 18 have real-world applications?
Yes, in situations involving proportions, such as dividing resources.
How can listing factors help find the GCF of 6 and 18?
By identifying the highest number that divides both without a remainder.
What are the factors of 6 and 18?
Factors of 6: 1, 2, 3, 6; factors of 18: 1, 2, 3, 6, 9, 18.
Can the Euclidean algorithm be used to find the GCF of 6 and 18?
Yes, divide 18 by 6 and use the remainder to find the GCF.
What common mistakes do students make when finding the GCF of 6 and 18?
Confusing GCF with LCM or overlooking the highest common factor.
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