107 LearnersLast updated on August 12, 2025
GCF of 14 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 14 and 35.
What is the GCF of 14 and 35?
The greatest common factor of 14 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 14 and 35?
To find the GCF of 14 and 35, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 14 and 35 by Using Listing of Factors
Steps to find the GCF of 14 and 35 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 14 = 1, 2, 7, 14.
Factors of 35 = 1, 5, 7, 35.
Step 2: Now, identify the common factors of them Common factors of 14 and 35: 1, 7.
Step 3: Choose the largest factor The largest factor that both numbers have is 7. The GCF of 14 and 35 is 7.
GCF of 14 and 35 Using Prime Factorization
To find the GCF of 14 and 35 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 14: 14 = 2 × 7 Prime Factors of 35: 35 = 5 × 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 14 and 35 is 7.
GCF of 14 and 35 Using Division Method or Euclidean Algorithm Method
Find the GCF of 14 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 14 35 ÷ 14 = 2 (quotient), The remainder is calculated as 35 − (14×2) = 7
The remainder is 7, not zero, so continue the process
Step 2: Now divide the previous divisor (14) by the previous remainder (7) Divide 14 by 7 14 ÷ 7 = 2 (quotient), remainder = 14 − (7×2) = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 14 and 35 is 7.
Common Mistakes and How to Avoid Them in GCF of 14 and 35
Finding GCF of 14 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 14, 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 indicates 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 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 14 and 35 Examples
Problem 1
A farmer has 14 apple trees and 35 orange trees. He wants to arrange them into equal rows with the largest possible number of trees in each row. How many trees will be in each row?
We should find GCF of 14 and 35 GCF of 14 and 35 7
There are 7 equal rows 14 ÷ 7 = 2 35 ÷ 7 = 5
There will be 7 rows, and each row gets 2 apple trees and 5 orange trees.
Explanation
As the GCF of 14 and 35 is 7, the farmer can make 7 rows. Now divide 14 and 35 by 7. Each row gets 2 apple trees and 5 orange trees.
Problem 2
A baker has 14 chocolate cupcakes and 35 vanilla cupcakes. She wants to pack them into boxes with the same number of cupcakes in each box, using the largest possible number of cupcakes per box. How many cupcakes will be in each box?
GCF of 14 and 35 7 So each box will have 7 cupcakes.
Explanation
There are 14 chocolate cupcakes and 35 vanilla cupcakes.
To find the total number of cupcakes in each box, we should find the GCF of 14 and 35.
There will be 7 cupcakes in each box.
Problem 3
A carpenter has 14 meters of pine wood and 35 meters of oak wood. He wants to cut both woods 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 14 and 35 The GCF of 14 and 35 7 The length of each piece is 7 meters.
Explanation
For calculating the longest length of the wood, first, we need to calculate the GCF of 14 and 35, which is 7. The length of each piece of wood will be 7 meters.
Problem 4
A gardener has two types of flowers, 14 roses, and 35 tulips. He wants to plant them in groups with the largest possible number of flowers in each group, without any leftover flowers. How many flowers will be in each group?
The gardener needs the largest group of flowers GCF of 14 and 35 7 The largest number of flowers in each group is 7.
Explanation
To find the largest number of flowers in each group of roses and tulips, 14 and 35, respectively, we have to find the GCF of 14 and 35, which is 7. The largest number of flowers in each group is 7.
Problem 5
If the GCF of 14 and ‘b’ is 7, and the LCM is 70, find ‘b’.
The value of ‘b’ is 35.
Explanation
GCF × LCM = product of the numbers
7 × 70 = 14 × b
490 = 14b
b = 490 ÷ 14 = 35
FAQs on the Greatest Common Factor of 14 and 35
1.What is the LCM of 14 and 35?
2.Is 14 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 35?
5.Are 14 and 35 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 14 and 35?
7.What are some fun ways kids in United States can practice GCF of 14 and 35 with numbers?
8.What role do numbers and GCF of 14 and 35 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 14 and 35 skills?
Important Glossaries for GCF of 14 and 35
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 14 are 1, 2, 7, and 14.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, and so on.
- 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 35 is divided by 14, the remainder is 7.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 14 and 35 is 70.
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.
