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100 LearnersLast updated on September 9, 2025
GCF of 55 and 77
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 55 and 77.
What is the GCF of 55 and 77?
The greatest common factor of 55 and 77 is 11. 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 55 and 77?
To find the GCF of 55 and 77, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 55 and 77 by Using Listing of factors
Steps to find the GCF of 55 and 77 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 55 = 1, 5, 11, 55. Factors of 77 = 1, 7, 11, 77.
Step 2: Now, identify the common factors of them Common factors of 55 and 77: 1, 11.
Step 3: Choose the largest factor The largest factor that both numbers have is 11. The GCF of 55 and 77 is 11.
GCF of 55 and 77 Using Prime Factorization
To find the GCF of 55 and 77 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 55: 55 = 5 x 11 Prime Factors of 77: 77 = 7 x 11
Step 2: Now, identify the common prime factors The common prime factor is: 11
Step 3: Multiply the common prime factors 11 = 11. The Greatest Common Factor of 55 and 77 is 11.
GCF of 55 and 77 Using Division Method or Euclidean Algorithm Method
Find the GCF of 55 and 77 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 55 77 ÷ 55 = 1 (quotient), The remainder is calculated as 77 − (55×1) = 22 The remainder is 22, not zero, so continue the process
Step 2: Now divide the previous divisor (55) by the previous remainder (22) Divide 55 by 22 55 ÷ 22 = 2 (quotient), remainder = 55 − (22×2) = 11 The remainder is 11, not zero, so continue the process
Step 3: Now divide the previous divisor (22) by the previous remainder (11) Divide 22 by 11 22 ÷ 11 = 2 (quotient), remainder = 22 − (11×2) = 0 The remainder is zero, the divisor will become the GCF. The GCF of 55 and 77 is 11.
Common Mistakes and How to Avoid Them in GCF of 55 and 77
Finding GCF of 55 and 77 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 55, 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 55 and 77 Examples
Problem 1
A gardener has 55 roses and 77 tulips. She wants to arrange them into bouquets with the same number of flowers in each bouquet, using the largest possible number of flowers per bouquet. How many flowers will be in each bouquet?
We should find GCF of 55 and 77 GCF of 55 and 77 = 11. There are 11 equal bouquets 55 ÷ 11 = 5 77 ÷ 11 = 7 There will be 11 bouquets, and each bouquet gets 5 roses and 7 tulips.
Explanation
As the GCF of 55 and 77 is 11, the gardener can make 11 bouquets.
Now divide 55 and 77 by 11.
Each bouquet gets 5 roses and 7 tulips.
Problem 2
A farmer has 55 apples and 77 oranges. He wants to package them into boxes with the same number of fruits in each box, using the largest possible number of fruits per box. How many fruits will be in each box?
GCF of 55 and 77 = 11. So each box will have 11 fruits.
Explanation
There are 55 apples and 77 oranges.
To find the total number of fruits in each box, we should find the GCF of 55 and 77.
There will be 11 fruits in each box.
Problem 3
A chef has 55 grams of salt and 77 grams of sugar. She wants to divide them into portions of equal weight, using the largest possible portion size. What should be the weight of each portion?
For calculating the largest equal weight, we have to calculate the GCF of 55 and 77 The GCF of 55 and 77 = 11. The portions are 11 grams each.
Explanation
For calculating the largest weight of the portions first we need to calculate the GCF of 55 and 77 which is 11.
The weight of each portion of salt and sugar will be 11 grams.
Problem 4
A carpenter has two wooden planks, one 55 cm long and the other 77 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 55 and 77 = 11. The longest length of each piece is 11 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 55 cm and 77 cm, respectively.
We have to find the GCF of 55 and 77, which is 11 cm.
The longest length of each piece is 11 cm.
Problem 5
If the GCF of 55 and ‘a’ is 11, and the LCM is 385. Find ‘a’.
The value of ‘a’ is 77.
Explanation
GCF x LCM = product of the numbers
11 × 385
= 55 × a 4235
= 55a a
= 4235 ÷ 55 = 77
FAQs on the Greatest Common Factor of 55 and 77
1.What is the LCM of 55 and 77?
2.Is 55 divisible by 5?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 77?
5.Are 55 and 77 prime numbers?
6.How can families in United States create number-rich environments to improve GCF of 55 and 77 skills?
7.What are some fun ways kids in United States can practice GCF of 55 and 77 with numbers?
8.What role do numbers and GCF of 55 and 77 play in helping children in United States develop problem-solving skills?
9.How can children in United States use numbers in everyday life to understand GCF of 55 and 77?
Important Glossaries for GCF of 55 and 77
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 11 are 1 and 11.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 11 are 11, 22, 33, 44, 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 77 are 7 and 11.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 77 is divided by 11, the remainder is 0 and the quotient is 7.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 55 and 77 is 385.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 55 and 77 will be 11, as it is their largest common factor that divides the numbers completely.
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.
