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105 LearnersLast updated on September 25, 2025
GCF of 77 and 56
The GCF is the largest number that can divide two or more numbers without leaving any remainder. It is used to share items equally, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 77 and 56.
What is the GCF of 77 and 56?
The greatest common factor of 77 and 56 is 7. 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 77 and 56?
To find the GCF of 77 and 56, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 77 and 56 by Using Listing of Factors
Steps to find the GCF of 77 and 56 using the listing of factors:
Step 1: Firstly, list the factors of each number Factors of 77 = 1, 7, 11, 77. Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56.
Step 2: Now, identify the common factors of them Common factors of 77 and 56: 1, 7.
Step 3: Choose the largest factor The largest factor that both numbers have is 7. The GCF of 77 and 56 is 7.
GCF of 77 and 56 Using Prime Factorization
To find the GCF of 77 and 56 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 77: 77 = 7 × 11 Prime Factors of 56: 56 = 2 × 2 × 2 × 7
Step 2: Now, identify the common prime factors The common prime factor is: 7
Step 3: Multiply the common prime factors The Greatest Common Factor of 77 and 56 is 7.
GCF of 77 and 56 Using Division Method or Euclidean Algorithm Method
Find the GCF of 77 and 56 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 77 by 56 77 ÷ 56 = 1 (quotient), The remainder is calculated as 77 − (56 × 1) = 21 The remainder is 21, not zero, so continue the process
Step 2: Now divide the previous divisor (56) by the previous remainder (21) Divide 56 by 21 56 ÷ 21 = 2 (quotient), remainder = 56 − (21 × 2) = 14
Step 3: Continue the process Divide the previous divisor (21) by the previous remainder (14) 21 ÷ 14 = 1 (quotient), remainder = 21 − (14 × 1) = 7
Step 4: Continue the process Divide 14 by 7 14 ÷ 7 = 2 (quotient), remainder = 14 − (7 × 2) = 0 The remainder is zero, the divisor will become the GCF. The GCF of 77 and 56 is 7.
Common Mistakes and How to Avoid Them in GCF of 77 and 56
Finding the GCF of 77 and 56 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 77, 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 77 and 56 Examples
Problem 1
A gardener has 77 rose bushes and 56 tulip plants. She wants to plant them in rows with the largest number of plants in each row. How many plants will be in each row?
We should find the GCF of 77 and 56 The GCF of 77 and 56 is 7. 77 ÷ 7 = 11 56 ÷ 7 = 8 Each row will have 7 plants.
Explanation
As the GCF of 77 and 56 is 7, the gardener can make rows with 7 plants each.
Now divide 77 and 56 by 7 to find the number of rows.
Problem 2
A chef has 77 apples and 56 oranges. He wants to prepare fruit baskets with an equal number of fruits in each basket. What is the maximum number of fruits he can have in each basket?
The GCF of 77 and 56 is 7. So each basket will have 7 fruits.
Explanation
To find the maximum number of fruits in each basket, calculate the GCF of 77 and 56.
There will be 7 fruits in each basket.
Problem 3
A school has two classes with 77 students and 56 students. They want to form groups with an equal number of students from each class. What should be the number of students in each group?
For calculating the equal number of students, we have to calculate the GCF of 77 and 56 The GCF of 77 and 56 is 7. Each group will have 7 students.
Explanation
For calculating the equal number of students in each group, first, we need to calculate the GCF of 77 and 56, which is 7.
The number of students in each group will be 7.
Problem 4
A parking lot has spaces for 77 cars and 56 bikes. They want to arrange the spaces in rows with the same number of spaces in each row, using the largest possible number of spaces per row. How many spaces will be in each row?
The parking lot needs the largest number of spaces in each row. The GCF of 77 and 56 is 7. The number of spaces in each row is 7.
Explanation
To find the largest number of spaces in each row, calculate the GCF of 77 and 56, which is 7.
The number of spaces in each row will be 7.
Problem 5
If the GCF of 77 and ‘b’ is 7, and the LCM is 616, find ‘b’.
The value of ‘b’ is 56.
Explanation
GCF × LCM = product of the numbers
7 × 616 = 77 × b
4312 = 77b
b = 4312 ÷ 77
= 56
FAQs on the Greatest Common Factor of 77 and 56
1.What is the LCM of 77 and 56?
2.Is 77 divisible by 7?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 56?
5.Are 77 and 56 prime numbers?
Important Glossaries for GCF of 77 and 56
- 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 7 are 7, 14, 21, 28, 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 14 are 2 and 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 21 is divided by 4, the remainder is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 77 and 56 is 616.
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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.
