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105 LearnersLast updated on September 24, 2025
GCF of 7 and 11
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 7 and 11.
What is the GCF of 7 and 11?
The greatest common factor of 7 and 11 is 1. The largest divisor of two or more numbers is called the GCF of the number.
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 7 and 11?
To find the GCF of 7 and 11, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 7 and 11 by Using Listing of Factors
Steps to find the GCF of 7 and 11 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 7 = 1, 7.
Factors of 11 = 1, 11.
Step 2: Now, identify the common factors of them Common factor of 7 and 11: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1.
The GCF of 7 and 11 is 1.
GCF of 7 and 11 Using Prime Factorization
To find the GCF of 7 and 11 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime Factors of each number Prime Factors of 7: 7 is a prime number itself, so its only prime factor is 7. Prime Factors of 11: 11 is a prime number itself, so its only prime factor is 11.
Step 2: Now, identify the common prime factors There are no common prime factors.
Step 3: In the absence of common prime factors, the GCF is 1. The Greatest Common Factor of 7 and 11 is 1.
GCF of 7 and 11 Using Division Method or Euclidean Algorithm Method
Find the GCF of 7 and 11 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 11 by 7 11 ÷ 7 = 1 (quotient), The remainder is calculated as 11 − (7×1) = 4 The remainder is 4, not zero, so continue the process
Step 2: Now divide the previous divisor (7) by the previous remainder (4) 7 ÷ 4 = 1 (quotient), remainder = 7 − (4×1) = 3
Step 3: Now divide the previous divisor (4) by the previous remainder (3) 4 ÷ 3 = 1 (quotient), remainder = 4 − (3×1) = 1
Step 4: Now divide the previous divisor (3) by the previous remainder (1) 3 ÷ 1 = 3 (quotient), remainder = 3 − (1×3) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 7 and 11 is 1.
Common Mistakes and How to Avoid Them in GCF of 7 and 11
Finding the GCF of 7 and 11 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 7, students may mention 2 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 the smallest common factor instead of the largest one. 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. While it is the only factor in this scenario, forgetting it shows an incomplete understanding of factors. Students should include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students confuse factors with 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 an even number
Students may assume that the GCF of two numbers will always be an even number. But it's not true; a GCF can also be an odd number. To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 7 and 11 Examples
Problem 1
A gardener has 7 rose bushes and 11 tulip bulbs. He wants to plant them in rows with the largest number of plants per row, ensuring each row has the same number of plants. How many plants will be in each row?
We should find the GCF of 7 and 11 GCF of 7 and 11 is 1.
There will be 1 plant in each row.
Explanation
As the GCF of 7 and 11 is 1, the gardener can only plant 1 plant per row to ensure each row has the same number of plants.
Problem 2
A chef has 7 apples and 11 oranges. He wants to create fruit baskets with the same number of fruits in each basket, using the largest possible number of fruits per basket. How many fruits will be in each basket?
GCF of 7 and 11 is 1.
So each basket will have 1 fruit.
Explanation
There are 7 apples and 11 oranges.
To find the total number of fruits in each basket, we should find the GCF of 7 and 11.
There will be 1 fruit in each basket.
Problem 3
A teacher has 7 notebooks and 11 pens. She wants to distribute them into kits with an equal number of items in each kit, using the largest possible number of items per kit. How many items should be in each kit?
For calculating the largest equal number of items per kit, we have to calculate the GCF of 7 and 11
The GCF of 7 and 11 is 1.
Each kit will have 1 item.
Explanation
For calculating the largest number of items per kit, we need to calculate the GCF of 7 and 11, which is 1.
Each kit will have 1 item.
Problem 4
A tailor has two pieces of fabric, one 7 meters long and the other 11 meters long. She wants to cut them into the longest possible equal pieces, without any fabric left over. What should be the length of each piece?
The tailor needs the longest piece of fabric GCF of 7 and 11 is 1.
The longest length of each piece is 1 meter.
Explanation
To find the longest length of each piece of the two fabric pieces, 7 meters and 11 meters, respectively,
we have to find the GCF of 7 and 11, which is 1.
The longest length of each piece is 1 meter.
Problem 5
If the GCF of 7 and ‘b’ is 1, and the LCM is 77, find ‘b’.
The value of ‘b’ is 11.
Explanation
GCF x LCM = product of the numbers
1 × 77 = 7 × b
77 = 7b
b = 77 ÷ 7 = 11
FAQs on the Greatest Common Factor of 7 and 11
1.What is the LCM of 7 and 11?
2.Is 7 a prime number?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 11?
5.Are 7 and 11 co-prime numbers?
Important Glossaries for GCF of 7 and 11
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 7 are 1 and 7.
- Prime Numbers: Numbers greater than 1 that have no divisors other than 1 and themselves. For example, 7 and 11 are prime numbers.
- Co-prime Numbers: Two numbers are co-prime if their greatest common factor is 1. For example, 7 and 11 are co-prime.
- Prime Factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 11 is 11.
- LCM: The smallest common multiple of two or more numbers is the LCM. For example, the LCM of 7 and 11 is 77.
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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.
