100 LearnersLast updated on August 5th, 2025
GCF of 5 and 7
The GCF (Greatest Common Factor) is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 5 and 7.
What is the GCF of 5 and 7?
The greatest common factor of 5 and 7 is 1. When 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 5 and 7?
To find the GCF of 5 and 7, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 5 and 7 by Using Listing of Factors
Steps to find the GCF of 5 and 7 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 5 = 1, 5.
Factors of 7 = 1, 7.
Step 2: Now, identify the common factors. Common factor of 5 and 7: 1.
Step 3: Choose the largest factor. The largest factor that both numbers have is 1. The GCF of 5 and 7 is 1.
GCF of 5 and 7 Using Prime Factorization
To find the GCF of 5 and 7 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number:
Prime Factors of 5: 5 = 5
Prime Factors of 7: 7 = 7
Step 2: Now, identify the common prime factors. There are no common prime factors.
Step 3: The GCF is the highest common factor, which is 1.
GCF of 5 and 7 Using Division Method or Euclidean Algorithm Method
Find the GCF of 5 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 5 7 ÷ 5 = 1 (quotient), The remainder is calculated as 7 − (5×1) = 2
The remainder is 2, not zero, so continue the process
Step 2: Now divide the previous divisor (5) by the previous remainder (2)
Divide 5 by 2 5 ÷ 2 = 2 (quotient), remainder = 5 − (2×2) = 1
The remainder is 1, so the process continues
Step 3: 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, the divisor will become the GCF.
The GCF of 5 and 7 is 1.
Common Mistakes and How to Avoid Them in GCF of 5 and 7
Finding the GCF of 5 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 5, students may mention numbers like 10 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 wrong factor as common. To avoid this confusion, students should list all factors and identify only the common ones.
Mistake 3
Forgetting to Include 1 as a Factor
Sometimes students may forget 1 as a common factor of the numbers. Although it does not affect the GCF, it shows an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse between 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 any two numbers is always greater than 1. But it's not true, especially for co-prime numbers. To avoid this, students should focus on common factors and understand that the GCF can be 1.
Greatest Common Factor of 5 and 7 Examples
Problem 1
A gardener has 5 sunflower plants and 7 rose plants. She wants to create equal groups of plants with the same number of each type in each group. How many plants will be in each group?
We should find the GCF of 5 and 7 GCF of 5 and 7 is 1.
There is 1 group.
5 ÷ 1 = 5
7 ÷ 1 = 7
There will be 1 group, with each group containing 5 sunflower plants and 7 rose plants.
Explanation
As the GCF of 5 and 7 is 1, the gardener can only make 1 group. Each group will have all the plants.
Problem 2
A teacher wants to distribute 5 notebooks and 7 pencils among students in such a way that each student gets the same number and type of items. What is the maximum number of students she can distribute these items to?
GCF of 5 and 7 is 1. So, each student can receive 1 notebook and 1 pencil, meaning the maximum number of students is 1.
Explanation
Since the GCF of 5 and 7 is 1, the maximum number of students that can equally receive the items is 1.
Problem 3
A baker has 5 chocolate muffins and 7 vanilla muffins. He wants to pack them into boxes such that each box has the same number of chocolate and vanilla muffins. How many muffins will be in each box?
For equal packing, find the GCF of 5 and 7
The GCF of 5 and 7 is 1.
Each box will have 1 chocolate muffin and 1 vanilla muffin.
Explanation
To pack the muffins equally in boxes, the GCF of 5 and 7 is 1, meaning each box can only contain 1 muffin of each type.
Problem 4
A chef has two different ingredients, one weighing 5 grams and the other weighing 7 grams. He wants to divide them into the longest possible equal portions without leftovers. What should be the weight of each portion?
The chef needs the longest portion GCF of 5 and 7 is 1.
The longest weight of each portion is 1 gram.
Explanation
To divide the ingredients into the longest possible portions without leftover, the GCF of 5 and 7 is 1, so each portion can weigh 1 gram.
Problem 5
If the GCF of 5 and ‘b’ is 1, and the LCM is 35, find ‘b’.
The value of ‘b’ is 7.
Explanation
GCF × LCM = product of the numbers
1 × 35 = 5 × b
35 = 5b
b = 35 ÷ 5 = 7
FAQs on the Greatest Common Factor of 5 and 7
1.What is the LCM of 5 and 7?
2.Is 5 a prime number?
3.What will be the GCF of two prime numbers?
4.What is the prime factorization of 7?
5.Are 5 and 7 co-prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 5 and 7?
7.What are some fun ways kids in United States can practice GCF of 5 and 7 with numbers?
8.What role do numbers and GCF of 5 and 7 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve GCF of 5 and 7 skills?
Important Glossaries for GCF of 5 and 7
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 5 are 1 and 5.
- Prime Numbers: Numbers that have only two distinct positive divisors: 1 and themselves. For example, 5 and 7 are prime numbers.
- Co-prime Numbers: Two numbers that have no common factor other than 1. For example, 5 and 7 are co-prime.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 7 is divided by 5, the remainder is 2.
- LCM: The smallest common multiple of two or more numbers. For example, the LCM of 5 and 7 is 35.
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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.
