103 LearnersLast updated on August 12th, 2025
GCF of 28 and 42
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 to schedule events. In this topic, we will learn about the GCF of 28 and 42.
What is the GCF of 28 and 42?
The greatest common factor of 28 and 42 is 14. 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 28 and 42?
To find the GCF of 28 and 42, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 28 and 42 by Using Listing of factors
Steps to find the GCF of 28 and 42 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 28 = 1, 2, 4, 7, 14, 28.
Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42.
Step 2: Now, identify the common factors of them Common factors of 28 and 42: 1, 2, 7, 14.
Step 3: Choose the largest factor The largest factor that both numbers have is 14.
The GCF of 28 and 42 is 14.
GCF of 28 and 42 Using Prime Factorization
To find the GCF of 28 and 42 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 28: 28 = 2 × 2 × 7 = 2² × 7
Prime Factors of 42: 42 = 2 × 3 × 7
Step 2: Now, identify the common prime factors The common prime factors are: 2 × 7
Step 3: Multiply the common prime factors 2 × 7 = 14.
The Greatest Common Factor of 28 and 42 is 14.
GCF of 28 and 42 Using Division Method or Euclidean Algorithm Method
Find the GCF of 28 and 42 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 42 by 28 42 ÷ 28 = 1 (quotient), The remainder is calculated as 42 − (28×1) = 14
The remainder is 14, not zero, so continue the process
Step 2: Now divide the previous divisor (28) by the previous remainder (14) Divide 28 by 14 28 ÷ 14 = 2 (quotient), remainder = 28 − (14×2) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 28 and 42 is 14.
Common Mistakes and How to Avoid Them in GCF of 28 and 42
Finding GCF of 28 and 42 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 28 and 42 Examples
Problem 1
A gardener has 28 rose bushes and 42 tulip plants. She wants to group them into equal sets, with the largest number of plants in each group. How many plants will be in each group?
We should find the GCF of 28 and 42 GCF of 28 and 42 2 × 7 = 14.
There are 14 equal groups 28 ÷ 14 = 2 42 ÷ 14 = 3
There will be 14 groups, and each group gets 2 rose bushes and 3 tulip plants.
Explanation
As the GCF of 28 and 42 is 14, the gardener can make 14 groups.
Now divide 28 and 42 by 14. Each group gets 2 rose bushes and 3 tulip plants.
Problem 2
A school has 28 basketballs and 42 soccer balls. They want to arrange them in rows with the same number of balls in each row, using the largest possible number of balls per row. How many balls will be in each row?
GCF of 28 and 42 2 × 7 = 14. So each row will have 14 balls.
Explanation
There are 28 basketballs and 42 soccer balls. To find the total number of balls in each row, we should find the GCF of 28 and 42. There will be 14 balls in each row.
Problem 3
A tailor has 28 meters of green fabric and 42 meters of blue 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 28 and 42 The GCF of 28 and 42 2 × 7 = 14. The fabric is 14 meters long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 28 and 42, which is 14. The length of each piece of fabric will be 14 meters.
Problem 4
A carpenter has two wooden planks, one 28 cm long and the other 42 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 28 and 42 2 × 7 = 14. The longest length of each piece is 14 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 28 cm and 42 cm, respectively, we have to find the GCF of 28 and 42, which is 14 cm. The longest length of each piece is 14 cm.
Problem 5
If the GCF of 28 and ‘a’ is 14, and the LCM is 84. Find ‘a’.
The value of ‘a’ is 42.
Explanation
GCF × LCM = product of the numbers
14 × 84 = 28 × a
1176 = 28a
a = 1176 ÷ 28 = 42
FAQs on the Greatest Common Factor of 28 and 42
1.What is the LCM of 28 and 42?
2.Is 28 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 42?
5.Are 28 and 42 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 28 and 42?
7.What are some fun ways kids in United States can practice GCF of 28 and 42 with numbers?
8.What role do numbers and GCF of 28 and 42 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 28 and 42 skills?
Important Glossaries for GCF of 28 and 42
- 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 4 are 4, 8, 12, 16, 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 28 are 2 and 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 5, the remainder is 2 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 28 and 42 is 84.
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.
