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102 LearnersLast updated on September 24, 2025
GCF of 28 and 40
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 28 and 40.
What is the GCF of 28 and 40?
The greatest common factor of 28 and 40 is 4.
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 40?
To find the GCF of 28 and 40, a few methods are described below -
Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm
GCF of 28 and 40 by Using Listing of Factors
Steps to find the GCF of 28 and 40 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 40 = 1, 2, 4, 5, 8, 10, 20, 40.
Step 2: Now, identify the common factors of them Common factors of 28 and 40: 1, 2, 4.
Step 3: Choose the largest factor The largest factor that both numbers have is 4.
The GCF of 28 and 40 is 4.
GCF of 28 and 40 Using Prime Factorization
To find the GCF of 28 and 40 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 28: 28 = 2 x 2 x 7 = 2^2 x 7 Prime Factors of 40: 40 = 2 x 2 x 2 x 5 = 2^3 x 5.
Step 2: Now, identify the common prime factors The common prime factor is: 2 x 2 = 2^2 Step 3: Multiply the common prime factors 2^2 = 4.
The Greatest Common Factor of 28 and 40 is 4.
GCF of 28 and 40 Using Division Method or Euclidean Algorithm Method
Find the GCF of 28 and 40 using the division method or Euclidean Algorithm Method.
Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 40 by 28 40 ÷ 28 = 1 (quotient), The remainder is calculated as 40 - (28×1) = 12 The remainder is 12, not zero, so continue the process.
Step 2: Now divide the previous divisor (28) by the previous remainder (12) Divide 28 by 12 28 ÷ 12 = 2 (quotient), remainder = 28 - (12×2) = 4.
Step 3: Now divide the previous divisor (12) by the previous remainder (4) 12 ÷ 4 = 3 (quotient), remainder = 12 - (4×3) = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 28 and 40 is 4.
Common Mistakes and How to Avoid Them in GCF of 28 and 40
Finding GCF of 28 and 40 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 9 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 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 28 and 40 Examples
Problem 1
A gardener has 28 roses and 40 tulips. She wants to arrange them into bouquets with each bouquet having the same number of flowers. What is the largest number of flowers she can have in each bouquet?
We should find the GCF of 28 and 40 GCF of 28 and 40 2^2 = 4.
There are 4 flowers in each bouquet.
Explanation
As the GCF of 28 and 40 is 4, the gardener can make bouquets with 4 flowers each.
Divide 28 and 40 by 4 to know how many bouquets can be made.
Problem 2
A coach has 28 soccer balls and 40 basketballs. He wants to group them into sets with the same number of balls, using the largest possible number of balls per set. How many balls will be in each set?
GCF of 28 and 40 2^2 = 4.
So each set will have 4 balls.
Explanation
There are 28 soccer balls and 40 basketballs.
To find the total number of balls in each set, we should find the GCF of 28 and 40.
There will be 4 balls in each set.
Problem 3
A baker has 28 cups of flour and 40 cups of sugar. She wants to divide them into packs of equal size, using the largest possible size. What should be the size of each pack?
For calculating the largest equal size, we have to calculate the GCF of 28 and 40, The GCF of 28 and 40 2^2 = 4.
Each pack will contain 4 cups of ingredients.
Explanation
For calculating the largest size of each pack, we first need to calculate the GCF of 28 and 40, which is 4.
The size of each pack will be 4 cups.
Problem 4
A tailor has 28 meters of blue fabric and 40 meters of red 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?
The tailor needs the longest piece of fabric GCF of 28 and 40 2^2 = 4.
The longest length of each piece is 4 meters.
Explanation
To find the longest length of each piece of the two fabrics, 28 meters and 40 meters, respectively.
We have to find the GCF of 28 and 40, which is 4 meters.
The longest length of each piece is 4 meters.
Problem 5
If the GCF of 28 and ‘b’ is 4, and the LCM is 280. Find ‘b’.
The value of ‘b’ is 40.
Explanation
GCF x LCM = product of the numbers 4 × 280 = 28 × b 1120 = 28b b = 1120 ÷ 28 = 40
FAQs on the Greatest Common Factor of 28 and 40
1.What is the LCM of 28 and 40?
2.Is 28 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 40?
5.Are 28 and 40 prime numbers?
Important Glossaries for GCF of 28 and 40
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 28 are 1, 2, 4, 7, 14, and 28.
- 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 28 are 2 and 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 13 is divided by 5, the remainder is 3 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 40 is 280.
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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.
