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112 LearnersLast updated on August 11, 2025
GCF of 16 and 28
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 16 and 28.
What is the GCF of 16 and 28?
The greatest common factor of 16 and 28 is 4. 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 16 and 28?
To find the GCF of 16 and 28, a few methods are described below - Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm
GCF of 16 and 28 by Using Listing of factors
Steps to find the GCF of 16 and 28 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 16 = 1, 2, 4, 8, 16.
Factors of 28 = 1, 2, 4, 7, 14, 28.
Step 2: Now, identify the common factors of them Common factors of 16 and 28: 1, 2, 4.
Step 3: Choose the largest factor The largest factor that both numbers have is 4. The GCF of 16 and 28 is 4.
GCF of 16 and 28 Using Prime Factorization
To find the GCF of 16 and 28 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 16: 16 = 2 × 2 × 2 × 2 = 24
Prime Factors of 28: 28 = 2 × 2 × 7 = 22 × 7
Step 2: Now, identify the common prime factors The common prime factors are: 2 × 2 = 22
Step 3: Multiply the common prime factors 22 = 4.
The Greatest Common Factor of 16 and 28 is 4.
GCF of 16 and 28 Using Division Method or Euclidean Algorithm Method
Find the GCF of 16 and 28 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 28 by 16 28 ÷ 16 = 1 (quotient), The remainder is calculated as 28 − (16×1) = 12 The remainder is 12, not zero, so continue the process
Step 2: Now divide the previous divisor (16) by the previous remainder (12) Divide 16 by 12 16 ÷ 12 = 1 (quotient), remainder = 16 − (12×1) = 4
The remainder is 4, not zero, so continue the process
Step 3: Now divide the previous divisor (12) by the previous remainder (4) Divide 12 by 4 12 ÷ 4 = 3 (quotient), remainder = 12 − (4×3) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 16 and 28 is 4.
Common Mistakes and How to Avoid Them in GCF of 16 and 28
Finding GCF of 16 and 28 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 28, 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 16 and 28 Examples
Problem 1
A gardener has 16 red roses and 28 white roses. She wants to arrange them into equal bunches with the largest number of flowers in each bunch. How many flowers will be in each bunch?
We should find the GCF of 16 and 28 GCF of 16 and 28 2 × 2 = 4. There are 4 equal bunches 16 ÷ 4 = 4 28 ÷ 4 = 7 There will be 4 bunches, and each bunch gets 4 red roses and 7 white roses.
Explanation
As the GCF of 16 and 28 is 4, the gardener can make 4 bunches. Now divide 16 and 28 by 4. Each bunch gets 4 red roses and 7 white roses.
Problem 2
A construction company has 16 large bricks and 28 small bricks. They want to stack them in rows with the same number of bricks in each row, using the largest possible number of bricks per row. How many bricks will be in each row?
GCF of 16 and 28 2 × 2 = 4. So each row will have 4 bricks.
Explanation
There are 16 large and 28 small bricks. To find the total number of bricks in each row, we should find the GCF of 16 and 28. There will be 4 bricks in each row.
Problem 3
A chef has 16 tablespoons of sugar and 28 tablespoons of flour. She wants to divide both into portions of equal size, using the longest possible length. What should be the size of each portion?
For calculating the longest equal size, we have to calculate the GCF of 16 and 28 The GCF of 16 and 28 2 × 2 = 4. The portion size is 4 tablespoons.
Explanation
For calculating the longest size of the portions first, we need to calculate the GCF of 16 and 28 which is 4. The size of each portion will be 4 tablespoons.
Problem 4
A designer has two pieces of fabric, one 16 meters long and the other 28 meters long. He wants to cut them into the longest possible equal pieces, without any fabric left over. What should be the length of each piece?
The designer needs the longest piece of fabric GCF of 16 and 28 2 × 2 = 4. The longest length of each piece is 4 meters.
Explanation
To find the longest length of each piece of the two pieces of fabric, 16 meters and 28 meters, respectively. We have to find the GCF of 16 and 28, which is 4 meters. The longest length of each piece is 4 meters.
Problem 5
If the GCF of 16 and ‘b’ is 4, and the LCM is 112. Find ‘b’.
The value of ‘b’ is 28.
Explanation
GCF × LCM = product of the numbers 4 × 112 = 16 × b 448 = 16b b = 448 ÷ 16 = 28
FAQs on the Greatest Common Factor of 16 and 28
1.What is the LCM of 16 and 28?
2.Is 16 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 28?
5.Are 16 and 28 prime numbers?
Important Glossaries for GCF of 16 and 28
- 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, 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 18 are 2 and 3.
- 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 16 and 28 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.
