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100 LearnersLast updated on October 25, 2025
GCF of 7 and 49
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 7 and 49.
What is the GCF of 7 and 49?
The greatest common factor of 7 and 49 is 7.
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 7 and 49?
To find the GCF of 7 and 49, a few methods are described below -
Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm
GCF of 7 and 49 by Using Listing of Factors
Steps to find the GCF of 7 and 49 using the listing of factors:
Step 1: Firstly, list the factors of each number Factors of 7 = 1, 7 Factors of 49 = 1, 7, 49.
Step 2: Now, identify the common factors of them Common factors of 7 and 49: 1, 7.
Step 3: Choose the largest factor The largest factor that both numbers have is 7.
The GCF of 7 and 49 is 7.
GCF of 7 and 49 Using Prime Factorization
To find the GCF of 7 and 49 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime factors of 7: 7 = 7 Prime factors of 49: 49 = 7 × 7 = 7².
Step 2: Now, identify the common prime factors The common prime factor is: 7.
Step 3: Multiply the common prime factor .
The greatest common factor of 7 and 49 is 7.
GCF of 7 and 49 Using Division Method or Euclidean Algorithm Method
Find the GCF of 7 and 49 using the division method or Euclidean Algorithm Method.
Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 49 by 7 49 ÷ 7 = 7 (quotient), The remainder is calculated as 49 − (7×7) = 0. The remainder is zero, so the divisor will become the GCF.
The GCF of 7 and 49 is 7.
Common Mistakes and How to Avoid Them in GCF of 7 and 49
Finding the GCF of 7 and 49 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 49, students may mention 14, 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 indicates an incomplete understanding of the factors.
Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse 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 a Prime Number
Students may assume that the GCF of two numbers will always be a prime number.
But it's not true that a GCF can also be a composite number.
To avoid this, students should focus on common factors rather than focusing on prime numbers.
Greatest Common Factor of 7 and 49 Examples
Problem 1
A gardener has 7 rose bushes and 49 daisy plants. She wants to plant them in equal groups with the largest number of plants in each group. How many plants will be in each group?
We should find the GCF of 7 and 49. GCF of 7 and 49 is 7.
There are 7 equal groups. 7 ÷ 7 = 1 49 ÷ 7 = 7, There will be 7 groups, and each group gets 1 rose bush and 7 daisy plants.
Explanation
As the GCF of 7 and 49 is 7, the gardener can make 7 groups. Now divide 7 and 49 by 7.
Each group gets 1 rose bush and 7 daisy plants.
Problem 2
A teacher has 7 notebooks and 49 pencils. She wants to distribute them equally among the students, with the largest number in each set. How many items will each student receive?
GCF of 7 and 49 is 7.
So each student will receive 7 items.
Explanation
There are 7 notebooks and 49 pencils.
To find the total number of items each student will receive, we should find the GCF of 7 and 49.
Each student will receive 7 items.
Problem 3
A chef has 7 apples and 49 oranges. He wants to create fruit baskets with the largest possible equal number of fruits in each basket. How many fruits will be in each basket?
For calculating the largest equal number of fruits, we have to calculate the GCF of 7 and 49. The GCF of 7 and 49 is 7.
Each basket will have 7 fruits.
Explanation
For calculating the largest number of fruits in each basket, we first need to calculate the GCF of 7 and 49, which is 7.
Each basket will have 7 fruits.
Problem 4
A craftsman has two pieces of wood, one 7 cm long and the other 49 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 craftsman needs the longest piece of wood. GCF of 7 and 49 is 7.
The longest length of each piece is 7 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 7 cm and 49 cm, respectively, we have to find the GCF of 7 and 49, which is 7 cm.
The longest length of each piece is 7 cm.
Problem 5
If the GCF of 7 and ‘a’ is 7, and the LCM is 49, find ‘a’.
The value of ‘a’ is 49.
Explanation
GCF × LCM = product of the numbers 7 × 49 = 7 × a 343 = 7a a = 343 ÷ 7 = 49
FAQs on the Greatest Common Factor of 7 and 49
1.What is the LCM of 7 and 49?
2.Is 7 a prime number?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 49?
5.Are 7 and 49 co-prime numbers?
Important Glossaries for GCF of 7 and 49
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 7 are 1 and 7.
- 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 factor of 49 is 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 7 and 49 is 49.
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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.
