GCF of 2 and 7
2026-02-28 08:40 Diff
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Last updated on September 18, 2025

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.

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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.

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?

Okay, lets begin

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.

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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?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

FAQs on the Greatest Common Factor of 2 and 7

1.What is the LCM of 2 and 7?

The LCM of 2 and 7 is 14.

2.Is 2 a prime number?

Yes, 2 is a prime number because it has only two factors: 1 and itself.

3.What will be the GCF of any two prime numbers?

The common factor of prime numbers is 1. Since 1 is the only common factor of any two prime numbers, it is the GCF of any two prime numbers.

4.What is the prime factorization of 7?

The prime factorization of 7 is simply 7, as it is already a prime number.

5.Are 2 and 7 prime numbers?

Yes, both 2 and 7 are prime numbers because they have only two factors: 1 and themselves.

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.