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104 LearnersLast updated on September 12, 2025
GCF of 36 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 schedule events. In this topic, we will learn about the GCF of 36 and 49.
What is the GCF of 36 and 49?
The greatest common factor of 36 and 49 is 1. 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, which are always positive.
How to find the GCF of 36 and 49?
To find the GCF of 36 and 49, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 36 and 49 by Using Listing of Factors
Steps to find the GCF of 36 and 49 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36. Factors of 49 = 1, 7, 49.
Step 2: Now, identify the common factors of them Common factors of 36 and 49: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 36 and 49 is 1.
GCF of 36 and 49 Using Prime Factorization
To find the GCF of 36 and 49 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 36: 36 = 2 × 2 × 3 × 3 = 2² × 3² Prime Factors of 49: 49 = 7 × 7 = 7²
Step 2: Now, identify the common prime factors There are no common prime factors.
Step 3: Since there are no common prime factors, the GCF is 1. The Greatest Common Factor of 36 and 49 is 1.
GCF of 36 and 49 Using Division Method or Euclidean Algorithm Method
Find the GCF of 36 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 36 49 ÷ 36 = 1 (quotient), The remainder is calculated as 49 - (36×1) = 13 The remainder is 13, not zero, so continue the process
Step 2: Now divide the previous divisor (36) by the previous remainder (13) Divide 36 by 13 36 ÷ 13 = 2 (quotient), remainder = 36 - (13×2) = 10
Step 3: Continue the process Divide 13 by 10
13 ÷ 10 = 1 (quotient), remainder = 13 - (10×1) = 3
Now divide 10 by 3 10 ÷ 3 = 3 (quotient), remainder = 10 - (3×3) = 1
Finally, divide 3 by 1 3 ÷ 1 = 3 (quotient), remainder = 3 - (1×3) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 36 and 49 is 1.
Common Mistakes and How to Avoid Them in GCF of 36 and 49
Finding the GCF of 36 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 8 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 greater than 1
Students may assume that the GCF of two numbers will always be greater than 1. But it's not true as numbers can be co-prime, so their GCF can also be 1. To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 36 and 49 Examples
Problem 1
A gardener has 36 roses and 49 tulips. She wants to plant them in rows with each row containing the same number of flowers. What is the largest number of flowers she can plant in each row?
To find the largest number of flowers in each row, we should find the GCF of 36 and 49.
The GCF of 36 and 49 is 1. So, each row will have 1 flower of either type.
Explanation
As the GCF of 36 and 49 is 1, the gardener can plant each flower individually in rows. Each row will only have 1 flower of either roses or tulips.
Problem 2
A baker has 36 chocolate chip cookies and 49 oatmeal cookies. She wants to pack them in boxes, with each box containing the same number of cookies. What is the largest number of cookies she can pack in each box?
The largest number of cookies in each box will be the GCF of 36 and 49.
The GCF of 36 and 49 is 1. So, each box will have 1 cookie of either type.
Explanation
The baker can only pack 1 cookie per box as the GCF of 36 and 49 is 1. Each box will contain either a chocolate chip cookie or an oatmeal cookie.
Problem 3
A library has 36 fiction books and 49 non-fiction books. They want to arrange them on shelves with each shelf containing the same number of books. What is the maximum number of books that can be arranged on each shelf?
To find the maximum number of books per shelf, we calculate the GCF of 36 and 49.
The GCF of 36 and 49 is 1. So, each shelf will have 1 book of either type.
Explanation
Each shelf can hold only 1 book because the GCF of 36 and 49 is 1. Thus, each shelf will contain either a fiction or a non-fiction book.
Problem 4
A teacher has two sets of cards, one with 36 cards and the other with 49 cards. She wants to divide them into groups with an equal number of cards in each group. What is the largest number of cards she can have in each group?
The largest number of cards in each group is the GCF of 36 and 49.
The GCF of 36 and 49 is 1.
So, each group will have 1 card of either type.
Explanation
The teacher can only have 1 card per group as the GCF of 36 and 49 is 1. Each group will contain either one of the 36 cards or one of the 49 cards.
Problem 5
If the GCF of 36 and ‘b’ is 1, and the LCM is 1764, find ‘b’.
The value of ‘b’ is 49.
Explanation
GCF × LCM = product of the numbers
1 × 1764 = 36 × b
1764 = 36b
b = 1764 ÷ 36 = 49
FAQs on the Greatest Common Factor of 36 and 49
1.What is the LCM of 36 and 49?
2.Is 36 a perfect square?
3.What will be the GCF of any two co-prime numbers?
4.What is the prime factorization of 49?
5.Are 36 and 49 co-prime numbers?
Important Glossaries for GCF of 36 and 49
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
- Co-prime Numbers: Two numbers are co-prime if their only common factor is 1. For example, 36 and 49 are co-prime.
- 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 49 are 7 and 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 49 is divided by 36, the remainder is 13.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 36 and 49 is 1764.
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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.
