100 LearnersLast updated on August 1st, 2025
GCF of 14 and 10
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 14 and 10.
What is the GCF of 14 and 10?
The greatest common factor of 14 and 10 is 2. The largest divisor of two or more numbers is called the GCF of the numbers. 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 10?
To find the GCF of 14 and 10, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 14 and 10 by Using Listing of Factors
Steps to find the GCF of 14 and 10 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 14 = 1, 2, 7, 14.
Factors of 10 = 1, 2, 5, 10.
Step 2: Now, identify the common factors of them Common factors of 14 and 10: 1, 2.
Step 3: Choose the largest factor
The largest factor that both numbers have is 2.
The GCF of 14 and 10 is 2.
GCF of 14 and 10 Using Prime Factorization
To find the GCF of 14 and 10 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 14: 14 = 2 x 7
Prime Factors of 10: 10 = 2 x 5
Step 2: Now, identify the common prime factors
The common prime factor is: 2
Step 3: Multiply the common prime factors
The GCF of 14 and 10 is 2.
GCF of 14 and 10 Using Division Method or Euclidean Algorithm Method
Find the GCF of 14 and 10 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 14 by 10 14 ÷ 10 = 1 (quotient)
The remainder is calculated as 14 − (10×1) = 4
The remainder is 4, not zero, so continue the process
Step 2: Now divide the previous divisor (10) by the previous remainder (4)
Divide 10 by 4 10 ÷ 4 = 2 (quotient), remainder = 10 − (4×2) = 2
The remainder is not zero, so continue
Step 3: Divide the previous divisor (4) by the previous remainder (2)
Divide 4 by 2 4 ÷ 2 = 2 (quotient), remainder = 4 − (2×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 14 and 10 is 2.
Common Mistakes and How to Avoid Them in GCF of 14 and 10
Finding the GCF of 14 and 10 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 6 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 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 that 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 10 Examples
Problem 1
A baker has 14 chocolate muffins and 10 blueberry muffins. She wants to arrange them into equal sets with the largest number of muffins in each set. How many muffins will be in each set?
We should find the GCF of 14 and 10 GCF of 14 and 10 is 2.
There are 2 muffins in each set. 14 ÷ 2 = 7
10 ÷ 2 = 5
There will be 2 muffins in each set, with 7 sets of chocolate muffins and 5 sets of blueberry muffins.
Explanation
As the GCF of 14 and 10 is 2, the baker can make sets with 2 muffins each. Now divide 14 and 10 by 2. Each set has 7 chocolate muffins and 5 blueberry muffins.
Problem 2
A gardener has 14 apple trees and 10 orange trees. He wants to plant them in rows with the same number of trees in each row, using the largest possible number of trees per row. How many trees will be in each row?
GCF of 14 and 10 is 2.
So each row will have 2 trees.
Explanation
There are 14 apple trees and 10 orange trees. To find the total number of trees in each row, we should find the GCF of 14 and 10. There will be 2 trees in each row.
Problem 3
A chef has 14 kilograms of flour and 10 kilograms of sugar. She wants to divide both into containers of equal weight, with the largest possible weight. What should be the weight of each container?
For calculating the largest equal weight, we have to calculate the GCF of 14 and 10
The GCF of 14 and 10 is 2.
Each container should weigh 2 kilograms.
Explanation
For calculating the largest weight of the containers, first we need to calculate the GCF of 14 and 10 which is 2. Each container will weigh 2 kilograms.
Problem 4
A carpenter has two wooden planks, one 14 cm long and the other 10 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?
The carpenter needs the longest piece of wood GCF of 14 and 10 is 2.
The longest length of each piece is 2 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 14 cm and 10 cm, respectively. We have to find the GCF of 14 and 10, which is 2 cm. The longest length of each piece is 2 cm.
Problem 5
If the GCF of 14 and ‘a’ is 2, and the LCM is 70. Find ‘a’.
The value of ‘a’ is 10.
Explanation
GCF x LCM = product of the numbers 2 × 70 = 14 × a
140 = 14a
a = 140 ÷ 14 = 10
FAQs on the Greatest Common Factor of 14 and 10
1.What is the LCM of 14 and 10?
2.Is 14 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 10?
5.Are 14 and 10 prime numbers?
6.How can children in United Arab Emirates use numbers in everyday life to understand GCF of 14 and 10?
7.What are some fun ways kids in United Arab Emirates can practice GCF of 14 and 10 with numbers?
8.What role do numbers and GCF of 14 and 10 play in helping children in United Arab Emirates develop problem-solving skills?
9.How can families in United Arab Emirates create number-rich environments to improve GCF of 14 and 10 skills?
Important Glossaries for GCF of 14 and 10
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 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 14 are 2 and 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 4, the remainder is 2 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 14 and 10 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.
