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101 LearnersLast updated on September 9, 2025
GCF of 56 and 96
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 96.
What is the GCF of 56 and 96?
The greatest common factor of 56 and 96 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 96?
To find the GCF of 56 and 96, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 56 and 96 by Using Listing of factors
Steps to find the GCF of 56 and 96 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 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.
Step 2: Now, identify the common factors of them Common factors of 56 and 96: 1, 2, 4, 8.
Step 3: Choose the largest factor The largest factor that both numbers have is 8. The GCF of 56 and 96 is 8.
GCF of 56 and 96 Using Prime Factorization
To find the GCF of 56 and 96 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 96: 96 = 2 x 2 x 2 x 2 x 2 x 3 = 2⁵ x 3
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 96 is 8.
GCF of 56 and 96 Using Division Method or Euclidean Algorithm Method
Find the GCF of 56 and 96 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 96 by 56 96 ÷ 56 = 1 (quotient), The remainder is calculated as 96 − (56×1) = 40 The remainder is 40, not zero, so continue the process
Step 2: Now divide the previous divisor (56) by the previous remainder (40) Divide 56 by 40 56 ÷ 40 = 1 (quotient), remainder = 56 − (40×1) = 16 The remainder is 16, not zero, so continue the process
Step 3: Now divide the previous divisor (40) by the previous remainder (16) Divide 40 by 16 40 ÷ 16 = 2 (quotient), remainder = 40 − (16×2) = 8 The remainder is 8, not zero, so continue the process
Step 4: Now divide the previous divisor (16) by the previous remainder (8) 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 96 is 8.
Common Mistakes and How to Avoid Them in GCF of 56 and 96
Finding GCF of 56 and 96 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 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 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 96 Examples
Problem 1
A gardener has 56 tulips and 96 roses. She wants to create equal bouquets, with the largest possible number of flowers in each bouquet. How many flowers will be in each bouquet?
We should find the GCF of 56 and 96 GCF of 56 and 96 2³ = 8. There are 8 equal bouquets 56 ÷ 8 = 7 96 ÷ 8 = 12 There will be 8 bouquets, and each bouquet gets 7 tulips and 12 roses.
Explanation
As the GCF of 56 and 96 is 8, the gardener can make 8 bouquets.
Now divide 56 and 96 by 8.
Each bouquet gets 7 tulips and 12 roses.
Problem 2
In a library, there are 56 novels and 96 magazines. The librarian wants to arrange them in stacks with the same number of books in each stack, using the largest possible number of books per stack. How many books will be in each stack?
GCF of 56 and 96 2³ = 8. So each stack will have 8 books.
Explanation
There are 56 novels and 96 magazines.
To find the total number of books in each stack, we should find the GCF of 56 and 96.
There will be 8 books in each stack.
Problem 3
A chef has 56 ounces of flour and 96 ounces of sugar. He wants to divide both into portions of equal weight, using the largest possible weight. What should be the weight of each portion?
For calculating the largest equal weight, we have to calculate the GCF of 56 and 96 The GCF of 56 and 96 2³ = 8. Each portion weighs 8 ounces.
Explanation
For calculating the largest weight of the portions, first we need to calculate the GCF of 56 and 96, which is 8.
The weight of each portion will be 8 ounces.
Problem 4
A builder has two metal rods, one 56 cm long and the other 96 cm long. He wants to cut them into the longest possible equal pieces, without any metal left over. What should be the length of each piece?
The builder needs the longest piece of metal GCF of 56 and 96 2³ = 8. The longest length of each piece is 8 cm.
Explanation
To find the longest length of each piece of the two metal rods, 56 cm and 96 cm, respectively, we have to find the GCF of 56 and 96, 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 672. Find ‘b’.
The value of ‘b’ is 96.
Explanation
GCF x LCM = product of the numbers
8 × 672
= 56 × b 5376
= 56b b
= 5376 ÷ 56 = 96
FAQs on the Greatest Common Factor of 56 and 96
1.What is the LCM of 56 and 96?
2.Is 56 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 96?
5.Are 56 and 96 prime numbers?
Important Glossaries for GCF of 56 and 96
- 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 8 are 8, 16, 24, 32, 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 56 are 2 and 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 96 is divided by 56, the remainder is 40 and the quotient is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 56 and 96 is 672.
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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.
