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102 LearnersLast updated on September 19, 2025
GCF of 56 and 72
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 56 and 72.
What is the GCF of 56 and 72?
The greatest common factor of 56 and 72 is 8. 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 56 and 72?
To find the GCF of 56 and 72, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 56 and 72 by Using Listing of Factors
Steps to find the GCF of 56 and 72 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56.
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
Step 2: Now, identify the common factors of them Common factors of 56 and 72: 1, 2, 4, 8.
Step 3: Choose the largest factor The largest factor that both numbers have is 8.
The GCF of 56 and 72 is 8.
GCF of 56 and 72 Using Prime Factorization
To find the GCF of 56 and 72 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 56: 56 = 2 x 2 x 2 x 7 = 23 x 7
Prime Factors of 72: 72 = 2 x 2 x 2 x 3 x 3 = 23 x 32
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 2 x 2 = 23
Step 3: Multiply the common prime factors 23 = 8.
The Greatest Common Factor of 56 and 72 is 8.
GCF of 56 and 72 Using Division Method or Euclidean Algorithm Method
Find the GCF of 56 and 72 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 72 by 56 72 ÷ 56 = 1 (quotient),
The remainder is calculated as 72 − (56×1) = 16
The remainder is 16, not zero, so continue the process
Step 2: Now divide the previous divisor (56) by the previous remainder (16)
Divide 56 by 16 56 ÷ 16 = 3 (quotient), remainder = 56 − (16×3) = 8
Step 3: Continue the process
Now divide 16 by 8 16 ÷ 8 = 2 (quotient), remainder = 16 − (8×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 56 and 72 is 8.
Common Mistakes and How to Avoid Them in GCF of 56 and 72
Finding the GCF of 56 and 72 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 56, 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 with 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 56 and 72 Examples
Problem 1
A farmer has 56 apples and 72 oranges. He wants to pack them into equal sets, with the largest number of fruits in each set. How many fruits will be in each set?
We should find the GCF of 56 and 72 GCF of 56 and 72 23 = 8.
There are 8 equal groups 56 ÷ 8 = 7 72 ÷ 8 = 9
There will be 8 groups, and each group gets 7 apples and 9 oranges.
Explanation
As the GCF of 56 and 72 is 8, the farmer can make 8 groups.
Now divide 56 and 72 by 8.
Each group gets 7 apples and 9 oranges.
Problem 2
A school has 56 desks and 72 chairs. They want to arrange them in rows with the same number of pieces in each row, using the largest possible number of pieces per row. How many pieces will be in each row?
GCF of 56 and 72 23 = 8.
So each row will have 8 pieces.
Explanation
There are 56 desks and 72 chairs.
To find the total number of pieces in each row, we should find the GCF of 56 and 72.
There will be 8 pieces in each row.
Problem 3
A tailor has 56 meters of cotton fabric and 72 meters of silk 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 56 and 72
The GCF of 56 and 72 23 = 8.
Each piece of fabric is 8 meters long.
Explanation
For calculating the longest length of the fabric first, we need to calculate the GCF of 56 and 72, which is 8.
The length of each piece of fabric will be 8 meters.
Problem 4
A carpenter has two wooden planks, one 56 cm long and the other 72 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 56 and 72 23 = 8.
The longest length of each piece is 8 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 56 cm and 72 cm, respectively, we have to find the GCF of 56 and 72, which is 8 cm.
The longest length of each piece is 8 cm.
Problem 5
If the GCF of 56 and ‘b’ is 8, and the LCM is 504. Find ‘b’.
The value of ‘b’ is 72.
Explanation
GCF x LCM = product of the numbers
8 × 504 = 56 × b
4032 = 56b
b = 4032 ÷ 56 = 72
FAQs on the Greatest Common Factor of 56 and 72
1.What is the LCM of 56 and 72?
2.Is 56 divisible by 4?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 72?
5.Are 56 and 72 prime numbers?
Important Glossaries for GCF of 56 and 72
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.
- Prime Factorization: A method of expressing a number as the product of its prime factors. For example, the prime factorization of 72 is 23 x 32.
- Euclidean Algorithm: A method for finding the greatest common divisor of two numbers by dividing and taking remainders repeatedly. For example, finding the GCD of 56 and 72 using this method gives 8.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 72 is divided by 56, the remainder is 16.
- LCM: The smallest common multiple of two or more numbers. For example, the LCM of 56 and 72 is 504.
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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.
