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102 LearnersLast updated on September 19, 2025
GCF of 7 and 35
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 35.
What is the GCF of 7 and 35?
The greatest common factor of 7 and 35 is 7. 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 35?
To find the GCF of 7 and 35, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 7 and 35 by Using Listing of factors
Steps to find the GCF of 7 and 35 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 7 = 1, 7.
Factors of 35 = 1, 5, 7, 35.
Step 2: Now, identify the common factors of them Common factors of 7 and 35: 1, 7.
Step 3: Choose the largest factor The largest factor that both numbers have is 7.
The GCF of 7 and 35 is 7.
GCF of 7 and 35 Using Prime Factorization
To find the GCF of 7 and 35 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 7: 7 = 7
Prime Factors of 35: 35 = 5 x 7
Step 2: Now, identify the common prime factors The common prime factor is: 7
Step 3: Multiply the common prime factors 7 = 7.
The Greatest Common Factor of 7 and 35 is 7.
GCF of 7 and 35 Using Division Method or Euclidean Algorithm Method
Find the GCF of 7 and 35 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 35 by 7 35 ÷ 7 = 5 (quotient),
The remainder is calculated as 35 − (7×5) = 0
The remainder is zero, so the divisor will become the GCF.
The GCF of 7 and 35 is 7.
Common Mistakes and How to Avoid Them in GCF of 7 and 35
Finding the GCF of 7 and 35 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 35, students may mention 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 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. 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 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 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 35 Examples
Problem 1
A farmer has 7 apple trees and 35 orange trees. He wants to plant them in rows with the largest possible number of trees in each row. How many trees will be in each row?
We should find the GCF of 7 and 35 GCF of 7 and 35 7.
So each row will have 7 trees.
Explanation
As the GCF of 7 and 35 is 7, the farmer can make rows of 7 trees.
Problem 2
A baker has 7 loaves of bread and 35 pastries. They want to pack them in boxes with an equal number of items, using the largest possible number of items per box. How many items will be in each box?
GCF of 7 and 35 7.
So each box will have 7 items.
Explanation
There are 7 loaves of bread and 35 pastries.
To find the total number of items in each box, we should find the GCF of 7 and 35.
There will be 7 items in each box.
Problem 3
A seamstress has 7 meters of silk and 35 meters of cotton fabric. She wants to cut both fabrics into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 7 and 35
The GCF of 7 and 35 7.
The fabric pieces will be 7 meters long.
Explanation
For calculating the longest length of the fabric first, we need to calculate the GCF of 7 and 35, which is 7.
The length of each piece of fabric will be 7 meters.
Problem 4
A gardener has two lengths of hose, one 7 meters long and the other 35 meters long. He wants to cut them into the longest possible equal pieces without any hose left over. What should be the length of each piece?
The gardener needs the longest piece of hose GCF of 7 and 35 7.
The longest length of each piece is 7 meters.
Explanation
To find the longest length of each piece of the two hoses, 7 meters and 35 meters, respectively, we have to find the GCF of 7 and 35, which is 7 meters.
The longest length of each piece is 7 meters.
Problem 5
If the GCF of 7 and ‘b’ is 7, and the LCM is 35, find ‘b’.
The value of ‘b’ is 35.
Explanation
GCF x LCM = product of the numbers
7 × 35 = 7 × b
245 = 7b
b = 245 ÷ 7 = 35
FAQs on the Greatest Common Factor of 7 and 35
1.What is the LCM of 7 and 35?
2.Is 7 a prime number?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 35?
5.Are 7 and 35 prime numbers?
Important Glossaries for GCF of 7 and 35
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 35 are 1, 5, 7, and 35.
- Prime Number: A number that has only two factors, 1 and itself. For example, 7 is a prime number.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 35 are 5 and 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 7 and 35 is 7, as it is their largest common factor that divides the numbers completely.
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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.
