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102 LearnersLast updated on September 18, 2025
GCF of 2 and 7
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 2 and 7.
What is the GCF of 2 and 7?
The greatest common factor of 2 and 7 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 2 and 7?
To find the GCF of 2 and 7, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 2 and 7 by Using Listing of Factors
Steps to find the GCF of 2 and 7 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 2 = 1, 2.
Factors of 7 = 1, 7.
Step 2: Now, identify the common factors of them Common factors of 2 and 7: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 2 and 7 is 1.
GCF of 2 and 7 Using Prime Factorization
To find the GCF of 2 and 7 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 2: 2 = 2
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 factors other than 1, the GCF is 1. The Greatest Common Factor of 2 and 7 is 1.
GCF of 2 and 7 Using Division Method or Euclidean Algorithm Method
Find the GCF of 2 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 2 7 ÷ 2 = 3 (quotient),
The remainder is calculated as 7 − (2×3) = 1
The remainder is 1, not zero, so continue the process
Step 2: Now divide the previous divisor (2) by the previous remainder (1)
Divide 2 by 1 2 ÷ 1 = 2 (quotient), remainder = 2 − (1×2) = 0
The remainder is zero, so the divisor becomes the GCF. The GCF of 2 and 7 is 1.
Common Mistakes and How to Avoid Them in GCF of 2 and 7
Finding the GCF of 2 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 7, students may mention 14 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. In this case, since 1 is the only common factor, it cannot be avoided. 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 tells about the 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 Always Greater Than 1
Students may assume that the GCF of two numbers will always be greater than 1. But it's not true; the GCF can also be 1, especially in the case of co-prime numbers like 2 and 7. To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 2 and 7 Examples
Problem 1
A gardener has 2 rose bushes and 7 tulip bulbs. She wants to plant them in such a way that each row has the same number of plants, with the maximum number of rows possible. How many plants will be in each row?
We should find the GCF of 2 and 7 GCF of 2 and 7 is 1.
There will be 1 plant in each row. 2 ÷ 1 = 2 rows 7 ÷ 1 = 7 rows
Each row will have 1 plant.
Explanation
As the GCF of 2 and 7 is 1, the gardener can make rows such that each row has 1 plant.
Now divide 2 and 7 by 1.
Each row has 1 plant.
Problem 2
A student has 2 notebooks and 7 pens. They want to distribute them into equal sets with the largest possible number of items per set. How many items will be in each set?
GCF of 2 and 7 is 1. So each set will have 1 item.
Explanation
There are 2 notebooks and 7 pens.
To find the total number of items in each set, we should find the GCF of 2 and 7.
There will be 1 item in each set.
Problem 3
A chef has 2 eggs and 7 apples and wants to create dishes using the same number of each ingredient per dish, maximizing the number of dishes. How many ingredients will be in each dish?
For calculating the number of ingredients in each dish, we have to calculate the GCF of 2 and 7
The GCF of 2 and 7 is 1.
Each dish will have 1 ingredient.
Explanation
For calculating the number of ingredients in each dish first we need to calculate the GCF of 2 and 7 which is 1.
Each dish will have 1 ingredient.
Problem 4
An artist has two canvases, one 2 meters wide and the other 7 meters wide. He wants to cut them into the longest possible equal pieces, without any canvas left over. What should be the width of each piece?
The artist needs the longest piece of canvas GCF of 2 and 7 is 1.
The longest width of each piece is 1 meter.
Explanation
To find the longest width of each piece of the two canvases, 2 meters and 7 meters, respectively.
We have to find the GCF of 2 and 7, which is 1 meter.
The longest width of each piece is 1 meter.
FAQs on the Greatest Common Factor of 2 and 7
1.What is the LCM of 2 and 7?
2.Is 2 a prime number?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 7?
5.Are 2 and 7 prime numbers?
Important Glossaries for GCF of 2 and 7
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 2 are 1 and 2.
- Prime Number: A number that has exactly two distinct positive divisors: 1 and itself. For example, 2 and 7 are prime numbers.
- Co-prime Numbers: Two numbers are co-prime if their GCF is 1. For example, 2 and 7 are co-prime numbers.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 7 is divided by 2, the remainder is 1.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 2 and 7 is 1, as it is their largest common factor.
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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.
