101 LearnersLast updated on August 5th, 2025
GCF of 14 and 16
The GCF 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 14 and 16.
What is the GCF of 14 and 16?
The greatest common factor of 14 and 16 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 16?
To find the GCF of 14 and 16, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 14 and 16 by Using Listing of Factors
Steps to find the GCF of 14 and 16 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 14 = 1, 2, 7, 14.
Factors of 16 = 1, 2, 4, 8, 16.
Step 2: Now, identify the common factors of them.
Common factors of 14 and 16: 1, 2.
Step 3: Choose the largest factor:
The largest factor that both numbers have is 2.
The GCF of 14 and 16 is 2.
GCF of 14 and 16 Using Prime Factorization
To find the GCF of 14 and 16 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 16: 16 = 2 x 2 x 2 x 2 = 24
Step 2: Now, identify the common prime factors.
The common prime factor is: 2
Step 3: Multiply the common prime factors 2.
The Greatest Common Factor of 14 and 16 is 2.
GCF of 14 and 16 Using Division Method or Euclidean Algorithm Method
Find the GCF of 14 and 16 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 16 by 14 16 ÷ 14 = 1 (quotient), The remainder is calculated as 16 - (14×1) = 2
The remainder is 2, not zero, so continue the process
Step 2: Now divide the previous divisor (14) by the previous remainder (2)
Divide 14 by 2 14 ÷ 2 = 7 (quotient), remainder = 14 - (2×7) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 14 and 16 is 2.
Common Mistakes and How to Avoid Them in GCF of 14 and 16
Finding GCF of 14 and 16 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 tells about the incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students confuse 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 16 Examples
Problem 1
A gardener has 14 tulips and 16 roses. She wants to plant them in rows with the same number of flowers in each row. What is the largest number of flowers that can be in each row?
We should find the GCF of 14 and 16.
The GCF of 14 and 16 is 2.
There will be 2 flowers in each row.
Explanation
As the GCF of 14 and 16 is 2, the gardener can plant 2 flowers per row.
Problem 2
A farmer has 14 apple trees and 16 orange trees. He wants to arrange them in the largest possible equal rows. How many trees will be in each row?
GCF of 14 and 16 is 2. So each row will have 2 trees.
Explanation
There are 14 apple and 16 orange trees.
To find the total number of trees in each row, we should find the GCF of 14 and 16.
There will be 2 trees in each row.
Problem 3
A baker has 14 loaves of sourdough bread and 16 loaves of rye bread. She wants to package them in boxes with the same number of loaves, using the largest possible number of loaves per box. How many loaves should be in each box?
For calculating the largest equal number of loaves, we have to calculate the GCF of 14 and 16.
The GCF of 14 and 16 is 2.
Each box will contain 2 loaves.
Explanation
For calculating the largest number of loaves per box, first, we need to calculate the GCF of 14 and 16, which is 2. The number of loaves in each box will be 2.
Problem 4
A student has two pieces of ribbon, one 14 cm long and the other 16 cm long. He wants to cut them into the longest possible equal pieces, without any ribbon left over. What should be the length of each piece?
The student needs the longest piece of ribbon.
GCF of 14 and 16 is 2.
The length of each piece is 2 cm.
Explanation
To find the longest length of each piece of the two ribbons, 14 cm and 16 cm respectively, we have to find the GCF of 14 and 16, which is 2 cm.
The longest length of each piece is 2 cm.
Problem 5
If the GCF of 14 and ‘b’ is 2, and the LCM is 112, find ‘b’.
The value of ‘b’ is 16.
Explanation
GCF x LCM = product of the numbers
2 × 112 = 14 × b
224 = 14b
b = 224 ÷ 14 = 16
FAQs on the Greatest Common Factor of 14 and 16
1.What is the LCM of 14 and 16?
2.Is 14 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 16?
5.Are 14 and 16 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 14 and 16?
7.What are some fun ways kids in United States can practice GCF of 14 and 16 with numbers?
8.What role do numbers and GCF of 14 and 16 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 16 skills?
Important Glossaries for GCF of 14 and 16
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.
- 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, 15, 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 10 are 2 and 5.
- 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.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 14 and 16 is 112.
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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.
