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102 LearnersLast updated on September 23, 2025
GCF of 6 and 7
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 6 and 7.
What is the GCF of 6 and 7?
The greatest common factor of 6 and 7 is 1. The largest divisor of two or more numbers is called the GCF of the numbers.
If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1.
The GCF of two numbers cannot be negative because divisors are always positive.
How to find the GCF of 6 and 7?
To find the GCF of 6 and 7, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 6 and 7 by Using Listing of Factors
Steps to find the GCF of 6 and 7 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 6 = 1, 2, 3, 6. Factors of 7 = 1, 7.
Step 2: Now, identify the common factors of them Common factor of 6 and 7: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 6 and 7 is 1.
GCF of 6 and 7 Using Prime Factorization
To find the GCF of 6 and 7 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 6: 6 = 2 x 3
Prime Factors of 7: 7 = 7
Step 2: Now, identify the common prime factors There are no common prime factors.
Step 3: Since there are no common prime factors, the GCF is 1.
GCF of 6 and 7 Using Division Method or Euclidean Algorithm Method
Find the GCF of 6 and 7 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 7 by 6 7 ÷ 6 = 1 (quotient), The remainder is calculated as 7 − (6×1) = 1
The remainder is 1, which is not zero, so continue the process
Step 2: Now divide the previous divisor (6) by the previous remainder (1) Divide 6 by 1 6 ÷ 1 = 6 (quotient), remainder = 6 − (1×6) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 6 and 7 is 1.
Common Mistakes and How to Avoid Them in GCF of 6 and 7
Finding the GCF of 6 and 7 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors. For example, while listing factors of 6, students may mention 4, which is incorrect. To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the Wrong Common Factor
Students may sometimes select an incorrect common factor. To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to Include 1 as a Factor
Sometimes students may forget 1 as a common factor of the numbers. However, it does not affect the GCF, but it indicates an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse factors and multiples. In that confusion, sometimes they may write multiples instead of factors. To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is Always Greater Than 1
Students may assume that the GCF of two numbers will always be greater than 1. But if the numbers are co-prime, the GCF can be 1. To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 6 and 7 Examples
Problem 1
A teacher has 6 apples and 7 oranges. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?
We should find the GCF of 6 and 7 GCF of 6 and 7 is 1.
There is 1 equal group. 6 ÷ 1 = 6 7 ÷ 1 = 7
There will be 1 group, and each group gets 6 apples and 7 oranges.
Explanation
As the GCF of 6 and 7 is 1, the teacher can make 1 group. Now divide 6 and 7 by 1. Each group gets 6 apples and 7 oranges.
Problem 2
A gardener has 6 red flowers and 7 blue flowers. They want to arrange them in rows with the same number of flowers in each row, using the largest possible number of flowers per row. How many flowers will be in each row?
GCF of 6 and 7 is 1.
So each row will have 1 flower.
Explanation
There are 6 red and 7 blue flowers. To find the total number of flowers in each row, we should find the GCF of 6 and 7. There will be 1 flower in each row.
Problem 3
A baker has 6 loaves of bread and 7 pastries. He wants to pack them into boxes of equal size, using the largest possible size. What should be the size of each box?
For calculating the largest equal size, we have to calculate the GCF of 6 and 7 The GCF of 6 and 7 is 1.
Each box will have 1 item.
Explanation
For calculating the largest size of the box, first, we need to calculate the GCF of 6 and 7, which is 1. The size of each box will be 1 item.
Problem 4
A carpenter has two wooden planks, one 6 cm long and the other 7 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?
The carpenter needs the longest piece of wood GCF of 6 and 7 is 1.
The longest length of each piece is 1 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 6 cm and 7 cm, respectively.
We have to find the GCF of 6 and 7, which is 1 cm. The longest length of each piece is 1 cm.
Problem 5
If the GCF of 6 and ‘a’ is 1, and the LCM is 42. Find ‘a’.
The value of ‘a’ is 7.
Explanation
GCF x LCM = product of the numbers
1 × 42 = 6 × a
42 = 6a
a = 42 ÷ 6 = 7
FAQs on the Greatest Common Factor of 6 and 7
1.What is the LCM of 6 and 7?
2.Is 6 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 7?
5.Are 6 and 7 prime numbers?
Important Glossaries for GCF of 6 and 7
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 6 are 1, 2, 3, and 6.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 7 are 7, 14, 21, 28, and so on.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factor of 6 is 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 7 is divided by 6, the remainder is 1 and the quotient is 1.
- Co-prime: Two numbers are co-prime if their GCF is 1, meaning they have no common factors other than 1. For example, 6 and 7 are co-prime.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
